Hi Tommo,
I'm sure that other people will have other suggestions but I have software called "Audioclean". Although I have only used it for transferring cassettes to mp3 it uses the same facility to transfer records. That it basically does is create a wav file from the sound generated (you need to connect your computer to the turntable to do this) and then you can process and clean up the signal before exporting as a mp3, ogg or whatever type of file you can select from the drop down menu. It really is very simple - there are things such as a vinyl equalisation button which removes hiss and boosts the lower frequencies as well as various other assorted settings that you can change.
It cost me about £25 - not long afterwards I saw it on sale in PC World for £20
Hope ths helps!