Process took 5+ months from beginning to end. Initially applied online back in February 2014 and just received word today that I got offered the position. After applying online, within a week I received an email to fill out an on-line background check and required to fax a paper. Simultaneously I scheduled a test to take at a semi-local college. If you want to know what the test is about, google it or see comments on here. After completion of that and almost immediate results, I heard nothing for easily 3+ months. During that time and till the end, online just said "In-process" & "Pre-screening"; this was very frustrating to say the least, and I gave up on it.
Roughly 3 weeks ago, I received an email asking me to do the background check on-line and faxing the form in again, along with scheduling an interview at my local post office. After completing that, I scored an interview after about 2-3 days. Interview was easy (see below), equivalent to them checking to see if you have a pulse honestly. Following the interview, I heard nothing and was slowly starting to drift away from remembering I applied.
Today I received a phone call from the HR rep and they offered me the job. Start orientation in 1 1/2 weeks, then it's off to being a pack mule! On a side note, all correspondence typically has a 3 day reply time to acknowledge the tasks they give you, so make sure to browse spam folder often to make sure. Also, make sure you research the test subjects and stuff, the last part can be tricky, as your test score means a lot on the waiting list.