1. Write to 5-6 professors stating your intent to apply for a PhD and mention about your research interests in brief. Also mention any projects/research you did with them or any classes you attended. Schedule an appointment to speak with them on phone or if possible, an in-person meeting. Wait patiently for them to reply. Contact their secretary about a week later if you don't receive a reply. Send a reminder email to them about 7-10 days later after your first email.
2. After the appointment has been scheduled, send them your academic transcripts, a draft version of your statement of purpose and a short resume so that the conversation would be meaningful.
3. Choose only those professors who know you well. Speak with 5-6 professors and convince 4-5 professors to write letters for you. Stay in touch with them throughout the application process and beyond.
4. Just keep re-writing and editing the statement till you feel comfortable. Most often, it'll continue till a week or two before the application deadline. Get it reviewed by your referees and others only after you've put sufficient effort yourself. Also, only incorporate those suggestions that you feel would actually help your statement.
Good Luck!