Night time

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For nighttime, the primary danger will be monsters. It is a good idea to stay in your lit shelter. If you don't have full iron armor and a sword, do not try to engage any monsters! The worst way to die early on is to be killed while trying to hunt monsters, so don't do it! Stay indoors at night!

One way to avoid being attacked by monsters is to put torches, glowstone, or a jack-o-lantern by your house. You will learn how to make all these things later on, but just a heads up. The torches are easy though, you just need to craft charcoal/coal on top of a stick.
If you are repeatedly getting killed, one desperate response is to go into "peaceful difficulty" (see "changing the rules", below). However, consider this: This being your first day, you aren't actually losing much by the deaths (at least not after what stuff you've gathered is lost), so you can just tough it out until dawn and start again.