Once you have found some people whose research interests you, it's time to write to them. I have had a number of profs tell me that they always like students to write about their own interests, so don't forget to include them. Remember, you are a separate person from your supervisor, with your own ideas and opinions and your own particular questions that you want answered.
Email is completely acceptable and many people think nothing of getting a letter electronically.
A few people have mentioned to me that they prefer getting a snailmail letter because they think it indicates an extra degree of interest and a willingness to take an extra step. I sent out snailmail letters initially, switching to email as deadlines approached. I was less interested in working with. In the long run, however, I doubt it makes any difference. Make sure you attach a c.v.