There are several ways to remove a rusted bolt. In this answer I am assuming that the person posting the question is properly differentiating between a nut and a bolt.

If the rusted bolt is embedded in, say, an engine block, one can sometimes dislodge it with penetrating oil like Liquid Wrench, although there are amny brans that do a similar job.

If that doesn't work, setting up a vibration by hitting the bolt head with a ball peen hammer might help break the rust bonds. Another method is to heat the block and the bolt with a propane or mapgas torch, the idea being that the differential in the heating and cooling rates of the two metals will cause the bonds to break.

During all of this, it is important to use a good quality wrench or socket set on the bolt head, If you strip or deform the head of the bolt, you will need to use what is commonly referred to as an easy out, a small tool which is cast sort of like a screw but wound counter clockwise instead. This is inserted in a hole which must be drilled down the center of the difficult bolt, and then the bit, inserted in a tap handle, is used to back the bolt out.

One last bit, if all else fails, sometimes you can drill the entire bolt out and then re-tap it with the next diameter bolt, or drill it oversize and use a Helicoil to re-line the bolt hole.