Soon after I passed my PMP exam on 27-June-2009, I saw this question at linkedin.com "How does one go about PMP? basic steps please..."
Rather than re-iterate the entire process which is very well defined in the PMI PMP credential handbook, here are some tips that should help.
1- Make a template to record your PjM experience. That will help organize and record uniform data for all projects.
2- The application need project supervisor information, like name, email and phone number. Be sure to get their permission.
3- Training courses can cost USA 5000.00 to less than USD 100.00. If you want to prepare on your own (like I did) you can chose the cheaper one which are usually online or podcasts. I used pmstudy.com.
4- PMI randomly audits submitted applications. So make sure you inform all relevant supervisors when you submit the application.
5- Read the PMBOK at least 2 times to get an understanding of the standard. The first time around, you may be amazed how different it appears from real life. The second time it all makes good sense.
6- Don't depend only on the PMBOK. Use other resources to prepare for the exam. Books, online prep questions, study groups, etc.
7- Books by Rita Mulcahy are most reccommended. I read it once, made notes and stuck with the notes for the final revision. A list of the books I read is given at the bottom.
8- Attempt lots and lots of practice questions. I can't stress this enough. There are several paid practice tests online. The pmstudy.com online course has almost 100 questions per topic, and a free practice test.
9- If you dont want to spend money on mock exams, make sure you practice with as many questions as possible. The internet is full of PMP sample questions.
10- If you are in doubt, ask for clarification. Join a study group. Linkedin has great professionals who are always willing to sharetheir experience and knowledge.
11- Most IMPORTANTly make sure the training, books, sample questions and mock exams are based on PMBOK 4th edition. All PMP exams from 1-July-2009 will be based on the 4th edition.
Some books I used:
PMP in Depth: Project Management Professional Study Guide for PMP and CAPM Exams - by Paul Sanghera (http://www.paulsanghera.com/books/pmp/index.html)
Head First PMP: A Brain-Friendly Guide to Passing the Project Management Professional Exam - by Andrew Stellman, Jennifer Greene (http://oreilly.com/catalog/9780596102340/)
PMP Exam Prep, Fifth Edition: Rita's Course in a Book for Passing the PMP Exam - by Rita Mulcahy (http://store.rmcproject.com/Detail.bok?no=42)