Learn Turkish: Eczaneden ilaç almam lazım. - I need to buy medicine from the pharmacy.

This is the standard way to express personal necessity in Turkish. You take the verb stem (al), add the short verbal noun ending (-ma), and then attach a possessive suffix to show who needs to do it. Here, the -m stands for "my". Literally, almam lazım means "my buying is necessary".

Why is the word for medicine just ilaç rather than the plural ilaçlar or the specific object ilacı?

When you are talking about buying a general, non-specific category of a thing, Turkish uses the plain, singular dictionary form. Adding the accusative case (ilacı) would mean "the specific medicine," and making it plural isn't needed when just stating the type of thing you are buying.

Doesn't the verb almak usually mean "to take"?

Almak is a very versatile verb! It means both "to take" and "to buy" depending on the context. Since you are getting something from a shop (eczane), "buy" or "get" is the most natural translation here.

Could I say eczanede instead of eczaneden?