Learn Swedish: Han lägger sig tidigt.

The verb lägger means "puts" or "lays", and sig is a reflexive pronoun meaning "himself". So literally, the sentence says "He lays himself early." Using att lägga sig (to lay oneself down) is the standard way to say "to go to bed" in Swedish.

How would I change this sentence to say "I go to bed early"?

You have to change both the subject and the reflexive pronoun so they match. Sig is only for the third person (he, she, it, they). For "I", the reflexive pronoun is mig. So you would say: Jag lägger mig tidigt.

Could I translate "goes to bed" directly by saying Han går till sängen?

You would only say that if you want to emphasize the physical walk towards a specific bed. To express the normal daily routine of turning in for the night, Swedes always use the reflexive phrase lägger sig.

Why does tidig (early) have a -t at the end to make it tidigt?

In Swedish, when you use a describing word (an adjective) to describe an action rather than a noun, you usually add a -t to the end. Here, tidigt describes the action of going to bed, so it gets that -t ending.