Removing old vinyl from a vehicle whether it's lettering or striping is not too bad once you figure out what you are dealing with. How old is the vinyl film? If it is all cracked and peeling you may need to use an eraser wheel. You can find these at Automotive Paint Supply stores. You will need a high RPM drill for use with the eraser wheel. As always read and follow the instructions when working with any power tool or the eye you poke out could be your own! These wheels rub the stripe off but will not hurt your paint if it is the original factory finish. If your vehicle has been repainted you will want to make sure the wheel will not hurt the paint before you go too far. I have always had good luck with these and they can save you hours of time. If the vinyl is still in good shape you have one of a few options. Vinyl can be easier to pull off if it is a nice sunny and warm day just let the sun warm up the side you want to work on. If it is cold out you will have to get the surface warm and dry. I use a heat gun for this, it gets hot in a hurry and I can move quickly. If you don't want to go that route you can use a hair dryer they work ok too. Once it is nice and warm to the touch pick an end or corner of the vinyl with your fingernail and get a hold of it. Then begin to to pull the vinyl back over the top of itself with a slow steady tension. It should just peel off. Sometimes there will be glue still stuck to the surface. You will have to get an adhesive remover to get the glue to give you a nice clean surface. 3M make a great automotive adhesive remover. It come in a 1 quart red and white can. I use a product called Pro Sol that works very well also.
I really should put up a video showing how this is done maybe later.