These words are known as "reductions" in the English language. There are several types of reductions (e.g cannot = can't, will not = won't, which are a form of reductions known as contractions) but the type you're asking about are reductions of a verb and "to". They're frequently used in informal English.
-Wanna
Formation: wanna = want + to
Usage: I wanna go to the park.
Meaning: I want to go to the park.
-Gonna
Formation: gonna = going + to
Usage: I'm gonna have to work late today.
Meaning: I'm going to have to work late today.
-Gotta
Formation: gotta = got + to
Usage: I gotta get up early in the morning.
Meaning: I got to get up early in the morning.
I hope this helps!