How can I avoid bubbles when applying an enormous sticker to plywood?
There are a number of methods to apply large decals and stickers to surfaces while avoiding bubbles and wrinkles.  

Most professionals prefer a wet method.  Clean the surface first. Then coat the surface, or the adhesive side of the sticker, or both, with slightly soapy water. Then lay it down slowly and use a squeegee while laying it down.  The soapy water enables you to lift it back up a little if you introduce a bubble or wrinkle.  The squeegee squeezes the soapy water out from under it.

A number of videos show the process, search for "decal wet method" or "vinyl wet application" for some.  I think http://www.youtube.com/watch?v=RSVk0C_NLpc is probably most applicable to your specific usage.

Also, ask the shop you're buying the decal from for their suggestions.

Note that unless you've purchased high quality plywood, and spent some time sanding, sealing, and filling, it's probably not going to be a very smooth surface anyway, and a high quality vinyl decal will look pretty lumpy on it.  Consider getting a better surface, or seeing if you can have a matte vinyl decal made, which reduces the glossy reflections which will show surface defects very clearly.