A very good question and a common one for folks who are very active in the development community. For starters, you can not apply, an existing MVP has to nominate you. It is good to discuss it with somebody like a regional director or MVP Lead or another MVP in your area so that folks know you are interested in becoming nominated. They can also give you advice on the kind of things you can work on, based on your personal background. One of the responsibilities of MVPs is to nominate other qualified potential MVPs. However, they have to be qualified, otherwise it is considered as a bit of a black mark if somebody nominates a friend who may not be very active. On the flipside, if somebody nominates somebody who has a lot of qualifications, it makes them look good.
There are two areas that are very important for becoming an MVP. One of them is to be very active. People that are awarded the designation of MVP are very active in the development community. They blog alot, give alot of presentations, answer questions on discussion boards, have websites, etc. They clearly do things that put them a cut above the rest. I am guessing that the first area is pretty self evident. I think that it is pretty much assumed that you have to get your name out there to be considered for an MVP. What is a bit lesser known is that it is important for you to have a wide variety of activities as well. For example, if you run a successful .NET website and it takes up all of your time, it will probably not be enough. It might seem like it should be, especially if it is a community oriented site and you invest alot of your into running it. However, the MVP program looks for people that are active in a number of other areas as well. They like to see well rounded contributions, such as blogging regularly and speaking at conferences or user groups. So, it is important to blog if you are not currently blogging, try to speak at events if you don't have many presentations under your belt, answer alot of questions on discussion boards, etc.
I hope that this helps and I will try to give more advice if you have any other questions. One of my goals of Community Credit is to create a tool to allow you to show off your contributions for a potential MPV application.