blastoff99. I suggest that for the quickest, easiest, and cheapest method, that you try the panel and trim adhesive that I posted about earlier.
The edge of plywood is a good substrate for that stuff to adhere to.
When I used it in my daughters old mobile home, she had painted the wood paneling, and I used it to put trim at the ceiling. I was worried at first, that once I put the piece up, it might need to be held in place so that it would not fall off before the adhesive held it up, but it did not sag. It was larger than what you are using, and it all stayed in place when I put it up. No nail holes to fill reduced the time involved too.
Part of the answer to what method you will employ depends on how much trim you intend to install. A small amount may not justify buying a small compressor, and nail guns.
Another part is what the trim stock is made out of. Oak would be more difficult to nail than pine or poplar. For painted trim, the new composite materials are easy to cut, nail paint, and are usually less costly than pine.
Drilling before nailing would only make sense if you are installing a small amount of oak, or other hard wood trim from a time, and labor standpoint.
I used the adhesive even though I have the electric, and pneumatic equipment to nail the trim because I wanted to see how well it worked, and since it was my daughters place, if it failed, it would not be like someone had paid me to do trim work in a fancy house, and I could just go back and fix it if there was a problem. This was a low budget mobile home fix-up, and we used lightweight composit trim, and painted over it. It worked to my satisfaction, and came out much better than any of the original trim that I did not replace.
If you intend to do a lot of trim, you should probably buy a small compressor, and a brad, and finish nailer package deal. I would not buy any of that stuff used, because the smaller, and lighter compressors are not lubricated, and buying used might get you one with a lot of miles on it. (I am a fanatic about tools, and always buy the better, or best, so maybe I am a little biased here, but I would not buy any Harbour Freight stuff, but brand name like Senco, Hitachi, Dewalt, etc).
Pre-drilling would be the last method I would use for anything more than one or two small windows.
I am not a finish carpenter, but I have remodeled a few houses, and have done a lot of fine woodworking.
Try the adhesive on one window, and let us know what you think.
Edit to add, that a milled-face hammer is not the correct hammer to use on finish nails. And, you should strike nails, or wood only with this type of hammer. If you strike other tools, like a nail set, chisel, or flat bar with a milled-face hammer, you will damage the hammer, and the other tool as well. The problem with using one on trim, is that instead of a flat smooth dent a regular hammer leaves from poor technique, the milled-face will leave a nasty waffle impression in your finish surface that will be harder to repair.
The best hammer to use for brads, and finish nails is what is known as a Warrington pattern. The ones I own are antique, and not labeled with a brand name, but I suspect were made in England at the turn of the 19th to the 20th century, and the shape of the head allows them to be used in very tight spaces by having a flat section in the round head like some modern framing hammers have. You can get close to a wall with this design.
Anyway, here is the type of hammer I would use for hand nailing trim:
Stanley Warrington Hammers - Lee Valley Tools