If you select the wrong paper for your needs, or choose a cheap (and light) paper, you may end up with a piece that is buckled and warped, or a paper that resists reworking. If you've already purchased a paper like this, all isn't lost. You can easily stretch your watercolor paper at home, with only a few easily found materials necessary.
I've found that I get the best results when working on 140lb paper that's been pre-stretched on a watercolor block. The block is a pad of watercolor paper that's glued on at least two edges, holding the attached paper taut and preventing it from buckling. Unfortunately, the needs of 7" Kara prevented me from working on a thick block of paper. I needed the ability to run my paper through my printer, so at the time, I opted for a 90lb cold pressed watercolor paper by Canson. Unfortunately, even though I'd 'stretched' it at the time (taped it down, saturated it with water, let it dry), I was still having issues with buckling. A little trial, error, and research revealed that I'd been stretching my watercolor paper all wrong.
How to Stretch Cheap Watercolor Paper
Your thin paper
Masonite board at least slightly larger than the paper itself. You want something a little bit absorbent, but won't warp with dampness. You also want to choose a board that allows you to continue working, because you won't remove your paper until the entire piece is finished.
Tape, like masking,drafting, or painter's. I like a 2" tape, as it leaves plenty of tape to grip the board.
A mop style brush capable of holding a lot of water.
Prepare your workspace. I recommend pencilling your image in ahead of time, especially if you print out bluelines, as there's a high chance that it'll get washed away. Have your strips of tape ready, and lay your paper on your board.
Wet down your paper. You want your paper to be completely saturated through, so that it'll stretch evenly. Although I haven't demonstrated it in this image, I usually saturate the backside first, and then spread it on the board, and soak the front. This allows better suction between my paper and the board, and usually results in a better job of stretching the paper.
EDIT: An intrepid Twitter follower took issue with my advice that you soak the paper, saying it would remove the sizing. I disagree. Many watercolor manuals suggest you even submerge the entire page in water for even distribution, which I don't do. Sizing is made of gelatin, which will dissolve in hot or warm water. You should never use hot or warm water with quality brushes because that will dissolve the glue holding the hairs in the ferrule, but cold water is fine. Same goes for sizing. My printmaking professor insuring undergrad, Cheryl Hayes, recommended that we soak out BFK Reeves for 10 minutes prior to printing so that it would print better. BFK is a high quality watercolor paper that one would be loathe to ruin, whereas I am suggesting a simple even saturation for cheap watercolor paper that would severely buckle if not properly stretched. Since my prior wording caused confusion, I am grateful that she pointed out her issue with this post, as it granted me an opportunity for clarification. Thank you, @OhComeOnAsh.
Apply additional water as necessary.
Sponge off excess water. You can use this as an opportunity to really press your paper down against the board. I usually roll a roll of paper towels across my page a few times. You're not attempting to dry out the paper, just dab up pools.
Wet down your tape strips, just enough so that they're damp, but not so much that they lose tackiness.
You'll have to work kinda fast to get all the tape down, and it'll have a tendency to twist on you. Once all four strips are down, you can dab away the excess water.
Let the paper dry fully (I usually let mine dry overnight).
You may end up with some buckling if you didn't properly saturate the paper.
You can try restretching the paper, but your results may be no better and the tape may tear the paper.
Once your paper has dried, you can begin applying washes if you so choose.