When used positively, なかなか means to be ‘very’, or ‘considerably’ something. However, when used in a sentence that has a verb in the ない (or ありません) form, it carries the meaning of ‘not at all’, ‘hardly’, or ‘far from’. Quite often, this expression is used to highlight something that the speaker expects should happen, but for some reason does/is not.
To use なかなか (or 中々（なかなか） in its kanji form), なかなか will be put at the beginning of a phrase (or directly before the negative verb), before further describing the situation.
-
先生（せんせい）、風邪（かぜ）がなかなか治（なお）らないんですけど、どうした方（ほう）がいいですか？
Doctor, my cold is hardly getting any better, what should I do?
仕事（しごと）が忙（いそが）しくて中々（なかなか）休（やす）みが取（と）れないんだよね。
Work is getting so busy that I can hardly take a day off.
As 中々（なかなか） just means the ‘middle’ of something, this expression can be thought of as highlighting that something is not in the ‘middle’ (optimal place to achieve a certain result). Due to this, it often expresses that the speaker wants something to be in that ‘optimal position’ but feels frustration due to the fact that it isn’t.
-
あいつなかなか来（こ）ないね。連絡（れんらく）もないし、俺（おれ）たちだけで行（い）こう。
He is not coming at all. Since he hasn't contacted us, let's just go without him.