I suggest downloading a program called Numark Cue, or Virtual DJ. Both are simple, easy to use programs that will allow you to do most to anything you want to do to mix. You can play around with it with your mouse and use your own mp3's to mix and its really fun too. Both programs are the same just different looks. Learn how to beat match, and drop beats and just play around wit hevery button on the programs and learn it all.
If you want to take it a little further, then look into getting a control board or a mixing board. this allows you to seamlessly mix two songs together, play with the level of bass and treble, and have some fun. there are some good examples here http://www.virtualdj.com/products/atomixmp3.html
they are called midi pads which is basically a piece of technology that allows you to use virtual dj and cue to its fullest. You can get a good one that will let you do a lot for around $80-$120. Or you can go ballin and get one for around $350-$500.
THEN if you really want to keep doing it, get some tables and get the Sarato vynil things that the guy above suggested. Thats basically what every DJ is going to, there are still those few out there that use real vynil but its sooo expensive, and really hard to find vynil. At that point your gonna need some good speakers, mixing board, two tables, a mean sound card, and some chedda cause shit gets expensive. Djing and mixing are serisouly a lot of money man and takes a lot of time to do some good with it all but its hella fun and when you have parties, chicks will be all over your junk.