Formal:
* Sto imparando l'italiano. (This is the most common and literal translation.)
* Sono in fase di apprendimento della lingua italiana. (This is a more formal and literal translation.)
* Studio l'italiano. (This is a more general statement, meaning you are studying Italian.)
Informal:
* Imparo l'italiano. (This is a more casual way to say it.)
* Sto imparando un po' di italiano. (This emphasizes that you are just starting to learn.)
More specific:
* Sto imparando a parlare italiano. (This means you are learning to speak Italian.)
* Sto imparando a leggere e scrivere in italiano. (This means you are learning to read and write in Italian.)
The best option for you will depend on the context and who you are talking to.