Learn Russian: Выход там.

The word там means "there" when we are talking about a fixed location (where something is right now). You use туда (to there) to show destination or movement, like if you were walking towards the doors. Since the exit itself isn't moving, it is located там (answering "where"), not туда (answering "to where").

Why isn't there a word for "is" in this sentence?

In Russian, the verb "to be" is almost always dropped in the present tense. Instead of saying "The exit is there", Russian simply says "Exit there". You just put the subject (выход) and its location (там) side by side.

How do we know it means "the exit" and not "an exit"?

Russian does not have articles like "the" or "a". The word выход can mean either "the exit" or "an exit" depending entirely on the situation. Since you are usually looking for a specific way out of a building, "the exit" is the most natural English translation here.

What if the exit is right next to me?

You would change the location word. Там means "there" (pointing away from you). If the exit is right next to you, you would use здесь or тут, which both mean "here".