The Deer Thing is a consumable item. You can use it at any time of the day in a Snow or an Ice Biome to summon the Deerclops. Be sure to use it in these biomes because if you do it in other biomes your item will be consumed and nothing will happen. You can craft it at an altar using 3 Flinx Furs, a Lens, and 5 Crimtane/Demonite Ores.
You can get the Deer Thing early in the game, but as the Deerclops is hard to defeat before defeating Skeletron, it is recommended to wait a little bit before trying to summon the Deerclops. Eventually, you can try to defeat it if you encounter him in a Snow Biome but don’t waste time collecting resources to craft the Deer Thing before defeating Skeletron.
The Deer Thing, as well as the Deerclops, is part of the Don’t Starve crossover.
How to get the Deer Thing easily
To craft the Deer Thing, you will have to get some Flinx Furs, a Lens, and some Crimtane or Demonite ores depending on your world’s evil.
To get Flinx Furs, you can go to an Ice Biome and try to find some Flinxs. They spawn mostly on the borders of the ice biome in caverns, and in chest rooms. They are quite easy to kill. As they have a high probability (more than 50%) of dropping between 1 and 3 Flinx Furs, the hardest thing actually will be to find Flinxs.
Then, to get a Lens, you just have to kill Demon Eyes. They are one of the most basic monsters so you probably have already met them. They spawn in the overworld at night. They have a 33% chance of dropping a Lens when killed.
Finally, you will have to find Crimtane or Demonite. You can find it in underground and mine it with at least a Gold Pickaxe. Or you can drop it from bosses as the Eye of Cthulhu, the Eater of Worlds (for demonite), or the Brain of Cthulhu.
Once you have all the required materials, just find an altar and you will be able to craft the Deer Things. You find altars in the Corruption Biome or in the Crimson Biome depending on your world’s evil. You can also find them in the Underground, but less frequently.