"He isn't here yet."
Translation:On tady ještě není.
Looking at the discussion that VladaFu linked to, I reached the following conclusion: "už" may refer to events that are anticipated. Thus, it might be translated as "finally": "Are we finally there?" On the other hand, the negation does not make sense, or at least it means something different: "He is not here finally."
Reacting because of your 20 in Spanish: If you know how to deal with ya and todavía /aún in positive, negative, and question contexts, take a detour between English and Czech via Spanish.
These Spanish words tend to correspond to Czech už and ještě, respectively, and conveniently point to all kinds of things in English as needed.