When you say albums, I take it you mean music recordings, as opposed to, say, photo albums?
If it's music albums, you'll need a LARGE hard disk to store them on, a soundcard with phono input (preferably, although mini jack is just about adequate), and a phono out on your stereo.
The software that comes with most soundcards is very basic, and may not do what you want it to.
For example, if you are recording vinyl or reels of tape, you may require some software that "cleans" the sound - by removing extraneous noise such as static pops, etc. There is cheap software that makes a good attempt at this, and there is expensive software that does this very well.
The other two things you'll need are a cable to connect your stereo out to the soundcard in, and a piece of recording software.
If your operating system is one of the Microsoft Windows family, then you have Sound Recorder, which is incredibly basic, but does the job.
There are many good music recording packages out there - I particularly like FastTrak's MP3 Professional.
You don't need an MP3 encoder, but it'll save you HUGE amounts of space;
A standard *.wav file, such as Sound Recorder creates, is about 40Mb in size, at high quality (and why would you want any other quality ;-)). An MP3 of that file would be about 4Mb, and the difference in quality is only noticeable by audiophiles.
If you are talking about photo albums, you'll need a LARGE hard disk, a scanner and some scanning software (most scanners come with reasonable software).
If you need any help, post back - I know there are many MP3 experts on this forum