Disclaimer; It's been some time since I've done this and things change. The following has been my experience when crossing the Canadian borders with groups. Have never done it as a solo so this may not apply. But your Canadian employer should walk you through what you need to do, or you may not show up.
For your gear; You'll need to create a manifest or carnet of the gear you're transporting to and from Canada; Item, brand, model, serial number, country of manufacture, value. When you enter Canada, declare your gear and present this manifest to the Customs agents. They'll eyeball your stuff (to some degree) and they should stamp the manifest, showing you entering with it. You have to declare that these are professional tools that you'll be using for the work you'll be doing while in Canada, then returning to the USA with them (not importing them into and selling them in Canada, tax and duty free.) You'll need to have the paperwork detailing your employment in Canada. Sometimes you'll be required to post a bond or deposit, depending on the amount, value of gear, duration of stay, etc. There are Border Bond companies that do this. They are not cheap.
Your Canadian employer should be well versed in this stuff, should be be able to walk you through it.
Also, there are work papers, likely withholding tax forms. This is stuff that the Canadian employer should be able to provide you with or help you with.
When you return to the USA, you need to get your manifest signed off on, showing that you did bring your gear back to the US, didn't sell it in Canada. If you have to post a deposit or bond, this is how you get your dough back.
US Customs can be dicks to musicians coming back from Canada. Be forthright and polite.
