The verbs that have to do with knowledge acquisition are complicated in Ukrainian. Because "вчити" is an imperfective verb, it means the action is incomplete. So "study" is a better English approximation because "learn" generally implies that the action is over and the knowledge has been successfully acquired.
To say "in one year," there would have to be the preposition за: Вона вивчила мову за один рік, or She LEARNED (and here I'm using a perfective verb, вивчити) the language IN one year.
Hope this helps.
Technically you can say "Вона вчилася мові один рік" as well.
The училася/вчилася is however a bit different verb. I'll try to explain the difference.
The key is in the "-ся" part which approximately can be translated as (-self). For example:
Вона вчилался один рік - She studied (improved herself) for one year Він учився на програміста - He studied (improved himself) to become a programmer
Вона вчилася писати один рік - she learned (improved herself) to write for one year.
When you have an object that is being studied (Math, Language, Biology etc.) then the best word to use is вчила (inf. вчити). For example:
Вона вчила математику один рік - She studied (what exactly?) Math for one year.
You can also say
Вона вчилася математиці один рік - (same meaning as above)
and that sounds also ok.