You will need:-
A means of connecting turntable to computer, the turntable must have 'line level' outputs if you are to connect it directly [or a pre-amp will be required].
Something like AUDACITY software, which can be downloaded for free, this can be used to sample the tracks of your LP/Singles. Save/Export them as MP3 or your preferred format.
I have also used Garage Band on MAC [free with OSX], just select 'real instrument' and remember to turn metronome off! Exports as MP4/192kb/s.
OR
For about 80 quid you can buy turntables that connect directly to your PC/Mac via USB - these come bundled with software.
OR
If you have got 400 notes to burn try :-
http://www.superfi.co.uk/index.cfm/page/moreinfo.cfm/Product_ID/4451
Burns an LP straight to a CD no PC needed!