I've e-mailed about 10 professors this cycle, and have been received positively by all of them including several skype interviews. The proper way to approach this, in my opinion, is to prepare a highly specific one page cover letter and CV (only important details: 1 page - education, pubs, short presentation list) and e-mail it to them. A simple sentence "Hi, I feel like I may be a good fit for your lab and to that end have attached my CV to this e-mail. If you have a moment to review, I would love to discuss potential opportunities to join your lab!" was how most of mine were structured.
The key is brevity, they're probably really busy and don't have much time to deal with this, but can skim a one page letter and CV in a few minutes and may be interested. On the whole I think they're just looking to see that you're really interested in them. Every professor would much prefer to take a student who has prior interest and knowledge than just someone rotating through at random.