Formal:
* J'habite dans un appartement. (This is the most common and neutral way to say it.)
Informal:
* Je suis en appartement. (This literally means "I am in an apartment," but it's understood to mean "I live in an apartment.")
* J'habite à l'appartement. (This is a more colloquial way to say it, and it's more common in some regions of France.)
Other options:
* J'habite en location. (This means "I live in a rented place," and it's useful if you want to specify that you are renting your flat.)
* J'habite dans un studio. (This means "I live in a studio apartment," and it's specific to a type of flat.)
The best option for you will depend on the specific situation and the level of formality you want to achieve.