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Lay down the tarp. Lay out all the parts of the tent on the tarp. Connect the tent poles. Insert the poles through the tent flaps. Raise the tent. Stake the tent to the ground. Connect the rain fly.
While most tents don't come with them, it's common to line the campsite with a plastic or vinyl tarp to provide a moisture barrier between the tent and the ground. While not necessary, strictly-speaking, it's recommended to use a camping tarp to keep moisture from leeching into the tent from below. If it rains, you'll be happy you've got this. Fold the tarp according to the shape of the tent, but slightly smaller. If there's any risk of rain, you don't want any of the corners sticking out. Don't worry about making it perfect, because you'll be able to tuck them under after you put up the tent. Remove all the components of the tent and inspect them to make sure everything is included and in good working conditions. You won't be able to set up a tent with some broken or missing tent poles, so it's good to take a minute to make sure everything is there. Each tent will be slightly different, depending on the size, style, and brand of the dome tent, but the basic components of newer dome tents should be mostly universal. You'll find:  The tent itself, which should be made of vinyl, plastic, and other materials, with a zippered opening and opening flaps where the tent poles will be inserted. The rain fly, which might look similar to the size and shape of the tent, but without the zippered openings and flaps for the tent poles. This is used to secure over the tent and offer a barrier from the rain, if necessary. Tent poles, which are generally connected with bungee chords or other stretchy material to keep them matched, but might not be with older tent poles, which might need to be screwed together. At the very least, there will be at least two and as many as five or six different poles, which will be made of several foot-long segments. You shouldn't need any tools to fix the tent poles together.  Stakes should be included to fix the tent to the ground, through small flaps at the base of the tent, and possibly on the rain fly. There should be between four and ten tent stakes. You might also want to include some kind of small hammer to fix them into the ground. Bungee ropes may also be included to fix the rain fly to the poles, or to fix the tent to the stakes. Each tent will be somewhat different. Put together, the tent poles should be six or ten feet long, snapped, fixed, or screwed together. All tent poles will be put together slightly differently, but most modern tent poles are connected with bungee ties that allow you to just snap them together without much effort. Fix them, so they're all put together, and then lay them on the ground flat. Flatten out the tent over the tarp and cross the tent poles over it, where they'll eventually go to make sure you've matched the right pole with the right location. The most basic tents will have to long crossing poles that will form an "X" pattern across the tent, passing through the flaps. When you're sure they're oriented correctly, push the pole through the flaps and leave them flat on the ground. Insert both poles. Different tents might have a few different sizes of poles, so you'll have to use your judgment to figure out which goes where, or consult the instructions. This can be the most difficult part of putting a tent together, if you don't have the instructions, but try to hold up the tent to see the basic shape of it, so see where they should go. Insert the tips of each pole into the eyelets at the end of each corner of the tent, to raise the tent and make it start taking shape. The poles should bend with some force, helping it to stand. It's usually much easier to do with a helper, standing opposite each other and bending each pole in tandem and helping hold it up. When you've got the poles staked, you might want to fluff it gently and pull the poles out slightly to let everything settle. Again, all dome tents will be slightly different. There should be little vinyl hoops or eyelets at each corner and in the center of each side of the tent, which you should use to stake the tent to the ground. Push the stake through and into the ground to secure the tent. If you're going to be sleeping in the tent immediately, you may choose to not stake it, especially if you're in an area with lots of coverage and low wind. If you're going hiking though, or the wind is up, it's usually important to stake the tent to the ground so it doesn't blow away. Fit the rain fly over the top of the tent and attach it to the tent. For some tents, the rain fly will be velcroed to the tent poles in different places, but on others it will be attached with bungee cords down to the stakes, stretching gently.  Some people choose to not put the rain fly on the tent, if they're sure it won't rain while you're camping. Some rain fly tarps will obscure your ability to see out the windows of the tent, which means you might leave it off it you want. It's usually better to be on the safe side, though, and put it on. After you've got the tent up, fold the corners of the tarp up and under the tent to make sure it's out of the way. Leaving any of it hanging out will promote water pooling underneath, if rains, so you want to make sure none of the tarp is showing.