As of current research, we are not really certain whether people are born with a certain ratio of slow twitch to fast twitch fibers and it stays that way, or if you can change that ratio through training. Muscular Hyperplasia is basically the process of splitting muscle fibers so that you end up having more. Hyperplasia is not proven, however many bodybuilders believe it is real.
What is proven (and a lot easier to do) is muscular hypertrophy. Hypertrophy is where, instead of your fibers multiplying, your fibers grow in size. I will cover the basics of hypertrophy in another article.
How you can use this knowledge to your advantage
Type I (slow twitch) muscle fibers are not very good at growing. It takes a lot of hard work and a lot of time for them to just grow a little bit. Type II fibers, however, grow very well. Almost all of your muscular hypertrophy will come from Type II muscle fibers. This means that training so that your muscles receive a lot of force for a very short period of time will target your Type II fibers, and therefore, stimulate muscular hypertrophy. It would be best to target both Type IIa and Type IIb fibers by training in a moderate rep range of about 8-12 reps for Type IIa and a lower rep range of about 3-6 for Type IIb.
However, there is more that goes into hypertrophy than just muscle fiber types, so please read my post about muscular hypertrophy to get the full picture.