How do I use a crimson/demon altar in Terraria?

The crimson/demon altar is a crafting station. You can use it to create early-game boss summoning items and the Night's Edge.

You use it like any other crafting station - simply stand next to it, open your inventory and click whatever item you need to craft.

It is simply a crafting station like any other in the game (work bench, anvil, etc.). To use it you just stand near it and open your crafting menu and you'll see the new options available pertaining to the demon altar.

If you don't see any new crafting options available in your crafting menu make sure you're standing close enough to it.

And don't feel dumb, the same thing happened to me the first time I found one!