Learn Turkish: Dükkândan meyve alıyorum. - I am buying fruit from the shop.

The word for shop is dükkân. The suffix for 'from' or 'out of' is either -dan or -den. Because the last vowel in dükkân is an a, A-type vowel harmony dictates that we use the -dan form to match it.

Doesn't alıyorum literally mean 'I am taking'?

Yes, it does! The root verb is almak (to take). However, in Turkish, using almak is the standard and most natural way to say 'to buy' when you are talking about getting something from a shop or store.

Why is there no word for 'some' or 'a' before meyve?

In Turkish, when you are talking about a general category of things (like buying fruit in general, rather than one specific piece of fruit), you just use the plain, naked noun. You don't need to add a word for 'some' or 'a'.

What is that little hat symbol over the 'a' in dükkândan?

That is a circumflex. It appears on some older borrowed words to show that the consonant before it (the k) should be pronounced with a softer sound. Luckily, it doesn't complicate our grammar here: we still treat it as an a for vowel harmony and use the -dan suffix!