What to watch out for when camping outdoors? What supplies need to be equipped?

Bug juice, itch treatment, sunscreen.

Some sleeping arrangement. Be sure to have a good thermal insulator between you and the ground even if it's summer.

Some arrangement for water and food.

Rain protection.

Having a place to sit can be a bonus. Even a "stadium chair" is better than nothing. 

If you don't have a toilet available, then you need to be able to dig a hole, to have bio-degradable toilet paper, and a way to clean your hands after toileting. 

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I carry a multiple boot  like BOBBER.

Not enough details.  What you need very much depends on where and WHEN.  A $30 sleeping bag from WalMart would be fine for Florida.  In Maine this time of year - that would get you killed.  

Depends on the type of camping, the region, and the season.

If you're camping out in Alaska in December, you better be prepared for harsh cold weather and be on the lookout for moose and grizzly bears.

If you're camping in the Arizona desert in August you better have plenty of water, a source of shade and be on the lookout for snakes & scorpions.

You will need a sleeping bag/ flashlight/tent/a ax or a saw. As well as food. I always carry a multiple to boot. Enjoy