Began with the online application--it's really long. Received an email a little less than a month later asking me to schedule a time to take the postal service exam 473E, an exam which focuses on delivery, distribution and retail. The exam consisted of a retail personality exam, as well as a skills test that test your abilities in regards to PO functions, including a memory test. The scores are available a few days later; I had an 87.9. Later on, I received an email that they would be beginning the background investigation, and they needed a bit of information. I also requested a copy of the report when they finished--I recommend doing so, it's really interesting to see what they find.
Just a little bit after that, I got a call for an in-person interview. Met at the hub PO in my hometown and met with the interviewer. Very basic interview for the most part, mainly behavioral questions. The interviewer placed a lot of emphasis on the particulars of the job, such as basically being on call in terms of shifts, as well as the stressfulness of the work. Went well overall.
About a month after that, I got an email to take a drug test. You can chose from places to go for the drug test near where you live, but you have to respond, schedule, and get it done within 5 days, I think. Pretty simple.