Quick answer
Estoy aprendiendo español
the everyday version
Hablo un poco de español
the alternative — see below for when
Which one to use
Estoy aprendiendo español uses the present progressive, which is exactly right for something ongoing. The language name stays lowercase.
Hablo un poco de español is the practical follow-up: it tells people your level and usually gets them to slow down. Adding ¿puedes hablar más despacio? makes that request explicit.
All the versions
Estoy aprendiendo español.I’m learning Spanish.
Hablo un poco de español.I speak a little Spanish.
Estoy empezando.I’m just starting out.
¿Puedes hablar más despacio?Can you speak more slowly? — informal.
Todavía cometo errores.I still make mistakes.
Where you are matters
In Spain the language is usually called <b>español</b> or <b>castellano</b>; <b>castellano</b> is also the normal word in Argentina and Chile.
Check yourself
How is the language name written in Spanish?