Getting a rusted nut off is often very difficult. Of course an air powered impact wrench such as you commonly find in a garage will help a lot. But for the rest of us?..
Penetrating oils exist that do a pretty good job of dissolving rust and releasing these things. Flood it on and vibrate it a bit, and if possible hold it in a position so that the oil flows into the rusted parts. Be patient and this will often work.
If not you will have to cut across the nut with a hack-saw and then maybe open it the rest of the way with a cold chisel.
The photos here shows you a "nut cutter", which actually forces a tempered blade right into the nut, and a new "adjustable wrench with a locking clamp" from Stanley. Both great tools to help tackle this problem.