Learn Turkish: Yağmur yağmadıkça kuyu kuruyor. - Unless it rains, the well dries up.

The suffix -dıkça means 'as long as'. When you attach it to a negative verb stem like yağma- (not rain), it literally means 'as long as it does not rain'. In English, we usually say 'unless it rains' to express this exact idea.

If I want to say 'unless you come', how do personal endings work with -mAdIkçA?

This suffix is a converb, meaning it turns the verb into an adverb, and converbs do not take personal endings. If you need to specify who is doing the action, you just use a pronoun. For example, 'unless you come' is simply sen gelmedikçe, leaving the verb suffix exactly the same.

I know yağmur means 'rain' (the noun), but why is the verb yağmak used with it? Doesn't that mean 'rain raining'?

Yes, literally it means 'rain raining'! In Turkish, precipitation requires both a noun subject and a verb. You cannot just use the verb yağmak on its own to mean 'it rains'; you must specify what is falling. So you say yağmur yağmadıkça (unless rain falls) or kar yağmadıkça (unless snow falls).

Why is the verb kuruyor in the present continuous tense (is drying) when the English translation says 'dries up'?

Turkish frequently uses the present continuous tense (-Iyor) for general facts, routines, and observable truths, where English prefers the simple present. You could also use the aorist tense here (kurur), but kuruyor is very natural in everyday speech for describing a process that happens regularly.