What is a padawan?
A padawan is someone who has an official master. Any Jedi Academy Knight or above can take on official padawans. He is to receive tutoring in the way of either one-on-one sessions, or padawan classes held by the higher ranking Jedi and attended by his apprentices.
How to become a padawan?
Those who were found touched by the Force and want to improve in it can choose to travel the Jedi Academy to receive proper training. Upon arrival, the individual is entitled as a Jedi Academy Student (abbreviated as JAS). It is customary that those without an official master are to call themselves JAS.
If the students feels that he needs more personal attention, he may seek a master. This can be done online or offline on the servers or website using the forums. Higher ranking Jedi are constantly on the lookout for new padawans. Those who have been recently promoted to Jedi Academy Knight do so too, but they need to know about the student's interest of looking for a master. There's a very useful pair of threads on the Academy's website called "Looking for a master?" and "Looking for a padawan?".