I know that the active is form by taking for example, lerni (to learn) and making it lernati, lerniti, or lernoti depending on the tense. My question is, how is the actived used and what is it for?

Bonvolu konsulti ĉapitron 23-an de la gramatiko en tiu paĝaro.

Please, look at chapter #23 of the grammar on this site.

SuperEsperanto1:I know that the active is form by taking for example, lerni (to learn) and making it lernati, lerniti, or lernoti depending on the tense. My question is, how is the actived used and what is it for?

Read the chapter Altebrilas recommends for an introduction.

From i-modo of a verb, e.g. lerni you can form participles both

in active

• present: lernant/
  
• past: lernint/
  
• future: lernont/

and passive voice

• present: lernat/
  
• past: lernit/
  
• future: lernot/

In theory these can be in any word class, but usually only adjectives and adverbs are used. Sometimes active participles can be nouns, when they usually denote a human, e.g. lernanto, one who is currently learning.

The adjective forms are mostly used to form compound verbs, kunmetitaj verboj, e.g. Mi estis lerninta, I was learning. However in contemporary Esperanto such forms are usually needed only to frame an other action, to give it a time frame.Mi estis lerninta, kiam vi alvenis, I was learning/studying, when you arrived. Using a compound verb form when you would use a continous verb form in English, makes you sound ,eh, unnatural.

The adverbial participles are used as shortened clauses, frazekvivalentoj, e.g. Mi legis libron manĝante pomon, I read a book while eating an apple.

While in theory you can create participal verbs, I recommend not to do so. They are overly complex, easy to misuse and easily misunderstood. See PMEG.