what type of vinyl are you using?
i also work in a graphic shop... and mostly around vinyl.
here is the thing.... it all depends on what type of vinyl you are using.
the basic kind of stuff from a place like vector or specialty material like 3ms controltac (its mostly used for automotiv wraps). control tac will forgive you pretty much any sin other than fire or cutting a big honking hole in it. it has fibers running through it like duct tape and spring back to its original shape with a little blast from a heat gun (not too much it will still melt!!!)
the regular day to day stuff... not so much.
mike deuce mentioned the squeegee (we call them hardcards in our shop) as shown can sometimes snag or flat out scratch and tear your regular vinyl unless its covered in something( the hard card... not the vinyl)... a sock will do.... i personally use that foam cushioning you put under table legs to keep them from ruining your floors.
if you must... use transfer.... its safer until you get used to it. laminating the graphic, if its printed and not die cut, is a godsend do it do it do it!!!!
the video mike posted is pretty much it... dont tug too hard on the ends though or you will seriously horribly warp image and wrinkle the graphic.
if you dont want to work the whole 2ft by 2 ft section at once you can run a line of duct tape down the center( tacking it to the mdf or what have you) then peel one half at a time work from the center to the edge. its an easy way to start working with vinyl if you arent sure what you are doing yet.
bubbles happen. practice with scrap until you feel comfortable. try it on coroplast, the worst surface ever for bubbles. if you can handle that your could wrap bea arthiurs bottom with nary a run, wrinkle or bubble.
watch out for dust and sandy debris. it will look like a bubble... but it wont come out once your tacked down and will look like crap forever. debris is your own fault.
dont apply it in the sun/ heat.... try to keep your application area reasonably cool. most materials will respond better, less curl, less bubbling on the plotter.
above all just dont be afraid of the vinyl. its not going to just fall apart... and you can buy it in 50 yard lengths or more, you can always print again. stay away from reflective though... that crap sucks ass.