I became interested in solving the Rubik's cube after I saw a cube program on Tom Davis's website (geometer.org) in October of 2003. The program has a tutorial with some group theory and basic cube moves in it. I did not have time for it until around December of 2003 before I dug out my old cube and tried to solve it. The first resolution of the cube took about 2 weeks. I was using the instructions that came with the cube but I couldn't make any sense out of it. Tom Davis's group theory manual came to my rescue. The top layer was resolved using basic commutators and conjugation. The first layer involved some 'common sense' and the second layer was solved using one basic algorithm and its reflection.
I messed around with the cube for a while and got to around 2 minutes. I was somewhat interested in how fast others can solve it and so I googled it on the web. To my amazement, there are people who can actually routinely solve it in 17 seconds (Jessica Fridrich)!! I felt that it was so impossible to attain but after watching a video on speedcubing.com of someone solving it in 16.48 seconds, I started speedcubing and got to around 20 seconds myself (after 2 months). I can frequently solve under 20 seconds now.
Another aspect of cubing that I got interested in recently is solving the cube blindfolded. Back then when I started cubing even solving with my eyes open proved to be difficult, so blindfold-cubing would be something of a miracle! But after messing around with it for a while I am now able to solve it blindfolded too. I started blindfold cubing around Aug 2005. My first successful solve occurred on my 4th try, with a time of 11 minutes 48 seconds including memorization. I can now routinely solve the cube blindfolded in a little over 2 minutes including memorization. You can find a video of me speedsolving the Rubik's cube and blindfold-solving it somewhere in this site (in the videos section).