The ford one will leave 2 holes, the gt wont. To get them off just use a putty knife working the emblem from all sides.. Im sure a lot of people will say use a string or some bs thatll take you forever because it wont scratch the car. I do many of these every day at work using the putty knife method and have yet to scratch a car doing so.
The ford one has 2 alignment pins on it so youre not going to be able to slide something under it all the way. Start on one edge, then the other, top, then bottom (any which order) until you hit the alignment pins then just pull it off by hand the rest of the way.
i took my GT badge off and all i used was some bug-b-gone and alcohol with a hair dryer and it came right off. cleaned it up really nice! i dont know if the oval Ford emblem has a hole behind it or not but if it does its easy to get filled.
Heres a pic of the fender holes. I prolly have one somewhere of the ones thatll be left on the decklid from the ford emblem too incase youre wondering before you take them off, the decklid pic prolly wont be as close up though.
i did this and removed the gt emblem then used some alchol to remove the stick residue then clayed it then a wax it look like it was never there use a plastic putty knife like amj said and do it slowly as for the ford you will have two holes after get them filled then have a body shop paint that section and blend it to match check out my garage pics it will look like it was never there