Ideally, you should be trying to connect 'line out' to 'line in'. (This will ensure that the power level produced by the record deck or amplifier is matched to the appropriate input level for the PC).
So look for anything labelled 'line out' on either the deck or the amplifier. (It might well be from a pair of phono sockets but other types of sockets are sometimes used). Then look for a 'line in' socket on the back of your PC. (It's usually a 3.5mm jack socket next to the microphone socket).
Head to your nearest branch of Maplin Electronics and purchase an appropriate lead to make the connection. You can find your nearest store, or buy online, here:
http://www.maplin.co.uk/
If you've not got a 'line out' socket, you could use the headphone socket of the amplifier but you should keep the volume set fairly low. If you've not got a 'line in' socket you could use the microphone socket. (Again, you should try to keep the input signal to a low level).
The most popular (free) software for sound recording (and editing) is probably Audacity:
http://audacity.sourceforge.net/
Chris