APPLICATION PROCESS; PART 1

Fly to the office; Hit the Join Button
Once you hit the 'join corp' button, this is the popup you'll get, and unless you put something in this box, the ceo won't be alerted to your application unless he/she checks his corporation panel regularly (which all CEOs and personnel managers should do by habit)

APPLICATION PROCESS; PART2a (simple)

Wait from the evemail that says your application has been accepted; Hit the Join button again; Done.

see step Part2b if you're not at a station with an office of the corp in question.

APPLICATION PROCESS; PART2b (complex)

You'll have to complete the 2nd step of the enlistment process once a high ranking officer replies to your application  (Once you get an ingame email, from the corp personnel manager, go into the corp window located on your icon menu, head to 'members', then 'my applications' and finally 'offers'- click accept if you see your application there)...that completes the process.