Hit (someone) up - to hit someone up means that you will contact them, without specifying how you’re gonna do that. You can call them, text them, send an email, Facebook, anything...
This is very commonly used and serves a great function.
By saying “hit me up” you’re not specifying the way you wish to receive contact, you’re letting the other person decide.
The closest word(s) to hit me up would be "contact me". But contact me is very formal and generally means to email someone, it’s generally used in a business setting.
For example:
“Alright man, I’ll hit you up on Saturday.”
“I’m going on vacation, I’ll hit you up when I get back.
Easy, isn't it?
And remember: PRACTICE BRINGS PERFECTION!
See ya...