I feel horrible. The woodgrain vinyl on the reproduction center dash trim piece I ordered (with gauges) wasn't actually stuck on all that well (sorry, Don), but I didn't care since I was going to peel it off anyway - I'm not a fan of the woodgrain, myself... so I went with 3M Di-Noc black carbon fiber vinyl. Love it a LOT better.
Anyway, David's got the right idea about test-fitting with the protective sheet still on, but go one step further and use a piece of butcher paper or similar to make the template, then transfer it onto a piece of poster board/card stock. Cut out the card stock template and trace onto the piece of woodgrain vinyl, cut to match, then it should slip right on without hassle.
As for prepping the piece, try not to get any paint on the areas where the vinyl will be installed - the adhesive on the vinyl will stick to the paint, but if the paint doesn't get good adhesion to the plastic, then your vinyl will come right up and take the paint with it. Also make sure the area where the vinyl is to be installed is absolutely butter smooth and hospital clean - any imperfections or objects stuck to the plastic will show through the vinyl as a tiny bump.
The best way to install the vinyl would be to get some sticker application gel, apply some to the clean and dry trim piece, peel off the protective sheet, apply a small amount to the adhesive side of the vinyl, then place the vinyl onto the piece. The gel will help you make small adjustments - sliding it around, rotating, etc. - and once it's properly positioned, use a credit card to 'squeegee' out the application gel, effectively taking any potential for air bubbles with it. The rest of the application gel will evaporate, and any residue is easily wiped away with water and mild glass cleaner. This technique works for any kind of vinyl being installed on pretty much any kind of smooth surface - that's how the exterior decals (such as the hockey stripes, Mach 1 emblems, et al) are applied.