Have a routine. Your routine will be different depending on personal preference, your level of playing and your goals. Pretty much all routines should include:
Play scales/arpeggios. It can be grueling and tedious, but repetition of scales and arpeggios is a key part of learning to play in tune. Make sure to practice all keys and different fingerings and practice with a metronome (and drone/tuner). Advice for making scale practice more fun:
play musically and beautifully
use different rhythms and bowings
challenge yourself to find new and useful fingerings
Published in 1881, this is the most commonly used method book out there. Simandl teaches the use of a "closed hand" 124 or 123 fingering pattern, dividing the fingerboard into 12 positions. Some newer books are extensions or modifications of the Simandl technique. Don't miss the Simandl 30 Etudes and Gradus ad Parnassum.
BillèNew Method for Double Bass
Published by Ricordi. There are a lot of books: Part I Volumes 1,2,3,4 and Part II Volumes 4,5,6 and an etude book 18 Studies in All Keys. For beginners, go with Part I Vol 1 (Ricordi 261) and for someone comfortable with the fingerboard up to the octave go with Part I Vol 3 (Ricordi 263). Ricordi 263 has a lot of very musical etudes in all keys which provide a good supplement to Simandl or other methods, and doesn't include anything in thumb position.
RabbathNouvelle Technique de la contrebasse
This method book is arguably the most distinct alternative to Simandl. Rabbath divides the fingerboard into six "positions" larger than the stretch of the hand, and each position is covered by pivoting. Rabbath also focuses attention on the bow. The method itself is controversial, but many players use pivoting in their playing.
Hans Sturm discusses Rabbath technique: 1, 2, 3, 4
Article by Jason Heath on Rabbath vs Simandl (and Vance): here and the follow-up here.
NannyComplete Method for the 4 and 5 stringed bass
StreicherMy way of playing the Double Bass
PetracchiSimplified Higher Technique
ZimmermanA contemporary concept of bowing technique for the double bass
A book of bowing exercises, excerpts and etudes, all built around the idea of practicing string crossings. This book catches a lot of criticism from some people (outdated, repetitive, aimless). Others find it very useful. Definitely not a substitute for Ševčík, but a supplement.
ŠevčíkSchool of Bowing Technique
A book of bowing exercises and etudes, meant to develop all aspects of bowing technique. The original work is for violin. There are various adaptations for bass: Robinson (Strokin') or Reinke or Tarlton or Gajdos. The last one is free to download. You can also freely download (and use effectively) the cello version.
Equipment
If you are a beginner shopping for a bass, check out the Beginner' Guide to Buying a Double Bass
Good intonation is something all bass player, even pros, must continually work on. Suggestions for working on intonation:
Practice scales and arpeggios routinely.
Play along with a drone (tonic + dominant preferably) to fix your pitch as you go. Set the drone on the tonic of your scale or the key of your etude. Some players say to be wary of relying on a drone. Discussion here and here.
Playing along with a tuner is also an option. Strobe tuners are better than any needle type, there are iPhone and Android strobe tuner apps.
Harmonics may also be used to check intonation. As an example, there are Harmonics on the G string where B, C, D, E, octave G and octave D are located. Since there may be a harmonic tone over a Wide space for a given note, lightly touch the string while bowing and move your finger to the spot where there is the least amount of vibration. That is the true harmonic. Press down on the string while bowing again and the resulting note will be in tune.
Be able to sing/hear the notes you are about to play. Doing this correctly will involve some ear training. See here and here for more on that.
Intonation in an ensemble is also about listening and adjusting, even if you think you are right. Listen for pitch around you and in other instruments of similar range (cellos and bassoons for example). Always remember that pianos and other keyboard instruments are not going to match what you are used to, which makes concertos difficult to play in tune and an exercise in compromise.
Listen to great opera singers. Try to observe how they Sustain notes, apply vibrato, use rubato and make cadences.
Go to live concerts where respected soloists are playing works from the repertoire.
Record yourself playing and criticize yourself.
Work slowly with a metronome so you understand the rhythm of what you're playing so you can be elastic with it when the time comes. One of the most common 'unmusical' pitfalls is not understanding how the rhythm changes organically in ritenutos etc..
Listen to great string players. Observing Heifitz, Cassals, Bashmet or Milstein will teach you much more about music than listening to most virtuoso bassists even if the bassists offer more technical information on where a particular note might be played. The sheer physical effort involved playing the double bass well consumes a large amount of energy which would otherwise be directed towards more 'musical' ends.
If you play well enough to be involved in chamber music try to work as closely with your fellow musicians as you can, duplicating phrasing and Dynamics, note lengths and accents etc.
Be flexible. Never assert that your interpretation is definitive.
If you play in a section where you are not the principal, try not only to copy the first players but to understand their philosophy through which they reach the decisions about how they play.
If you are lucky enough to be a principal bassist try to encourage your players to be with you emotionally, and psychologically as well as physically. Praise good work and try to find out why things go wrong when they do and fix them.
Be yourself! Know your limitations and don't tackle works way beyond your level. Playing an easy piece musically is so much better than playing a difficult piece badly!
Playing fast passages
There are basic approaches to playing an unapproachable passage. Before trying any, you should (tentatively) decide on a fingering/bowing. You can of course adjust these decisions as you go. A metronome is essential here.
Begin at a very slow tempo, slow enough that you can play the passage without struggling, tensing up, or doing other things that you wouldn't normally do.
Play through the passage at this tempo until it feels comfortable.
Add rhythmic variations at this tempo. For example, if you are playing quarter notes, replace the quarter note with a dotted eight + sixteenth note. Do other variations too.
Kick up the metronome a couple clicks and return to step 1. When building up speed, you should use very little left hand contact, trying to emulate the amount of contact you would have at Full tempo. With this amount of contact, the bow speed should be slower and the notes should not speak as well as you would expect at a slow tempo.
Begin reasonably close to the performance tempo. Again make sure that you are not tense or struggling as you play. The idea of the following is to emphasize the fact that every single note of the passage is important; each note has a beginning and an end.
Play just the first note of the passage, imagining the passage continuing after you play.
Play the first two notes of the passage, then play the first three notes of the passage, then the first four, etcetera, until you have played the whole passage.
Return to step 1, but begin on the second note of the passage instead. Next time through, begin on the third note, etcetera.
Smart use of a metronome can make it less annoying and more useful. There are two basic uses for a metronome:
Developing good rhythm. The ultimate goal of metronome use here is to internalize rhythm (and tempo) so that you can play rhythmically without the metronome or play purposely outside of a steady beat. Here are some tips for doing this:
First and most basic idea: set the metronome on the beat that you feel the time rather than a further subdivision. Do the subdivision in your head.
Set the metronome on the largest subdivision possible (halfs, whole bars or even multiple bars). Further subdivision should be done in your head.
Set your metronome on the backbeat (beats 2 and 4 of a 4/4 pattern for example). For some reason this especially helps if you are rushing 16th or faster note patterns. Be careful not to start playing rock and roll or you'll never get a job.
Put the click on a funny beat in the measure, like 4, or even the and of 2. See here.
Play tough subdivisions of the beat. For instance, with your metronome beating quarters, play a scale or etude on quarter note triplets (three notes to 2 clicks) or play quarter notes with the metronome beating half note triplets (4 notes to 3 clicks). You can make this exercise really hard if you try.
Play just in front or just behind the beat. That is, play as if the click is coming a split second earlier or later than it actually is. It is useful to be able to do this in orchestra for various reasons (pushing without accelerating or playing in time with an instrument that is far away for example).
Use just the blinking light on your metronome, no sound.
Developing good timing. The idea here is to make sure that the the notes you play begin and end at the right place. Some ideas for practice:
Basic détaché stroke exactly with the metronome.
String crossings exactly with the metronome.
Longer notes with a rest in between. Make sure that you start and stop exactly in rhythm.
Short Series of spiccato notes with rests in between. Focus on a Clean and even start and finish.
Metronome set at higher subdivision to make sure that your rhythm doesn't become "lazy" (make sure those dots or double dots don't drift into triplets or vice versa).
There are many ways to learn and practice vibrato. It can be taught as a rocking motion: moving sharp then flat around the desired pitch. In lower positions this rocking comes from the arm, not the wrist. In thumb it can come more from flexibility in the wrist. It can also be taught similar to violin vibrato: sliding sharp then flat around the note with no pressure. Pressure is gradually applied until it sounds like vibrato. The vibrato motion is the same as the shifting motion. More reading here and here and here.
An exercise for starting out: here. General suggestions:
practice rhythmic vibrato with a metronome (slow and fast)
practice different "width" vibrato
practice maintaining vibrato through shifts and finger changes (playing scales or vomits for example)
don't forget to try vibrating on your thumb
generally, vibrate "around" the pitch rather than "up to it" (this is a little controversial)
listen to singers and other strings for musical ideas
It's hard to be a good player if you don't have something/someone to emulate. You should build a basic listening library. Here are some recordings that a lot of people think are good. Most of them are relatively cheap, and some of them are historically significant.
Serge Koussevitzky, bass player and conductor of the Boston Symphony from 1924-1949, wrote this concerto in 1902 (supposedly with orchestration help from R. Gliére) and premiered it in 1905.
Written by Johann Baptist Vanhal in the 1770's for the bassist Johannes Sperger. It is usually performed in D major or C major (E major or D major solo tuning).
This suite is originally in C major, and is sometimes played at cello pitch. More often it is transposed to G major (see International edition Ed Bernat, for example). Bourrées I and II from this suite are very common audition pieces.
Bozo Paradzik 1st mvmt, 2nd and 3rd mvmt. This version is the "original composers version", played in D major, but an octave higher than a beginner would want to play it.
Zbigniew Borowicz 1st mvmt (this is at the pitch most students would play)