Learn Turkish: Liseden beri gitar çalıyorum. - I have been playing the guitar since high school.

The word beri (since) always needs the 'from' ending (the ablative case, -den or -dan) on the word before it. So, to say 'since high school', Turkish literally says 'from high school since' (liseden beri).

The translation says 'have been playing'. Why does Turkish just use the present continuous tense çalıyorum?

English uses 'have been doing' for an action that started in the past and is still happening now. Turkish is much simpler! You just use the standard present continuous tense (-yor) together with a time phrase like -den beri to show the action is still ongoing.

Why is it just gitar and not gitarı? Doesn't it need the specific object ending?

Because we are talking about playing the guitar in general, not a specific, physical guitar that we were already discussing. When talking about a general category, skill, or habit like this, Turkish leaves the noun in its plain, dictionary form.

I remember çalmak meaning something else. What else does it mean?

You might remember it meaning 'to steal' or 'to ring' (like a bell or a door). The verb çalmak has a few different meanings depending on context, but when it is paired with a musical instrument, it always translates as 'to play'.