Changing a processor?
You need to figure out what kind of socket your processor goes into. Some of the P4 3.2 GHz processors are in socket LGA 775 and others are socket 478. If it's an LGA 775 then you can use most of the Core 2 Duo processors. The best way to check compatibility (and the socket type) is to look up your motherboard and see what processors it can accept.
Changing a processor?
Like RingoSk said before make sure the mobo is compatible with a core 2 (maybe you'll have to do a bios update) . After you'll install it is gonna work just like that lol.
