The event setup given by Bloodmorph is correct. But like Shaz said, it's better not to use a Parallel Process for this kind of thing. An event that you can interact with to run the check on your EXP and give you the appropriate skills will take far less of your system resources than a Parallel Process.
If it's important to be able to run the event from anywhere, you could use an Autorun Common Event, by setting a switch at the beginning of every battle, and having that switch be a condition for the Autorun Common Event that checks your EXP and grants skills if appropriate, before setting the switch back to OFF so it doesn't run more than once per end-of-battle. (You could even do this for a PP Common Event, but that's dicey because it means other processing can run while the event is running - which, in rare cases, could cause two of your events to try to do something to a character at the same time and cause bizarre behavior. Autorun is usually the better option for this kind of thing. PP events should only be used when something needs to be done while other action is happening outside the event.)
One thing that's maybe being overlooked in this topic - you can already learn skills by leveling up (with EXP), on the "Classes" tab of the database. Maybe there's a reason you don't want this to happen automatically and you want the player to have to visit the teacher to learn the skills, or maybe you're trying to separate levels from skills - but if that's not the case, yeah, "Classes" is the easiest way to do it.