The End is a unique place. Once you kill the Ender Dragon, you may even want to live there, or you could take an extra challenge and try to survive the Ender Dragon's wrath in the End dimension!
First Hand End Survival
If you want to live in the end with/without the Ender Dragon, you would need wood. Wood is the basis of all tools, weapons, and ultimately life itself! Food is also needed greatly. Bring a diamond pickaxe so you can mine obsidian.
Normal End Survival
First, find a suitable spot to set up your base. It would be wise to place your first base near the End Exit portal. Grab a dirt block you harvested from the Overworld and build a tree farm. Once your first tree has grown, start thinking about tools. Once you have a tool set, you could start thinking about an actual roof over your head.
End Survival Shelters/Homes
Digging down would be my first choice. You can make your base as large as you want it to be if you make it underground. The only bad thing about this shelter is you could have a risk of falling out of the world and into the Void.
Obsidian Pillar Shelter
Another good survival shelter is inside an obsidian pillar. This is a good home because it can have multiple floors and (depending on which pillar you chose to live in) it is very spacey! The cons, however, might outweigh the pros. Obsidian, as we know very well, is very hard to break quickly. It would be a long and weary process, one that requires the usage of a Diamond Pickaxe.
Ender Dragon Survival
If you really want another challenge, you should try this! Surviving in the End alone should be challenging enough, but the Ender Dragon makes this even harder. Be prepared to die a lot!
Basic Dragon Avoiding
When you first enter the End, the Ender Dragon will be after you. Run around the surface of the End for the first couple minutes. Tip: Know where the dragon is at all times. Do not let the dragon hit you! Above all, don't let the End Dragon hit you into the Void. Your gear will be irretrievable.
Basic Endermen Protection
The Ender Dragon is not the only danger in this floating spit of sand. The Endermen also pose a threat! Always bring 2 or more water buckets with you so whenever the endermen walk into it, they get hurt and teleport away. And as always, bring some great armor!