put a stud in the insert and you use some pliers to grip it and pull it. IF all works, the stud will pull the insert out as well if you use enough force.
Oh, God, No! Not unless you plan on throwing away the stud! Not only that, put if you side-pull the insert enough (not pulling straight up), it will elongate/enlarge the hole.
This is very easy: Get yourself a 6mm phillips-head bolt, about 1-1/2" in length (gotta be longer than the insert), and a stack of fender washers (a stack, again, taller than an insert), with center holes larger than the o.d. of the inserts. Grab one with a smaller center hole, too (You'll see in a sec). If it's a flatmount trem, you simply stack the washers over the insert in question, with the smaller-hole washer on top of the stack. Insert the bolt down through the stack, and thread it into the insert. Take your phillips screwdriver, and start "tightening" the bolt. As you do, it will pull the insert out of the hole.
Now, in the case of a recessed trem, you will have to ensure two opposite sides of the insert are level with each other, so that the washers stack perpendicular to the top face of the body. I usually just use some thick scraps of plexiglass, that I have lying around. But the procedures still the same. I've been trialfitting all the parts on my upcoming project, like this, and it makes things super-simple.
Oh, and if you have a drill press, it really comes in handy as an arbor press, to push those inserts in , for ya. MUCH easier than pounding away on the friggin things with a hammer and block. Yikes!