Melinda, 

Some French verbs require a following preposition either before a noun, a verb infinitive, or in both situations. Mostly à or de ( some verbs use either, with or without a change in meaning ), but some verbs require other prepositions. There is no specific rhyme or reason to which verbs require a preposition - it needs to be ‘ learnt/acquired’ as you go ( Trying to learn lists without context is relatively futile, in my view ). 

‘Apprendre qqc (Noun) - learn something 

 ‘ Apprendre qqc (Noun) à qqn ‘ - teach someone something ( or inform/tell someone of/about something )

‘Apprendre à faire qqc (verb infinitive) - learn (how) to do something.

French and English verbs are used differently - the need for a preposition following the verb is determined by the verb ‘being followed’ ( apprendre in this example) , and not by the infinitive (danser in this example).

Although an English infinitive includes a preposition, the French infinitive does not. Don’t confuse the ‘English translation’ as being exactly the same as ‘ the meaning of something French in French’, or an indicator of the same pattern of use - they are not quite the same thing, sometimes considerably different ! 

This is a large area of learning in French - too big to cover comprensively in a QandA response. Some links below to start with and then to follow other links as suits you best presently. If you have follow up questions, will try to help if I can.

 https://french.kwiziq.com/revision/glossary/verbal/infinitif-infinitive

 https://www.lawlessfrench.com/grammar/verbs-with-a/

 https://www.wordreference.com/fren/apprendre