Choose in what you want to soak your paper. A tray or a bathtub are quite suitable. Just remember - you have to clean it thouroughly first (especially the bathtub - be sure there is no residue of a soap, condicioners, etc.). An ordinary detergent you use for your dishes is good enough for the task.
Get your materials ready - you don't want to loose time when you're actually stretching the paper.
1. A paper you want to stretch - it's good to leave some surplus paper around your chosen size so you could attach the tape.2. A wooden board.
3. An ordinary brown tape. I like to cut it beforehand (again, saving time).
4. Tissues or paper towels for wiping excessive moisture.
5. A bowl with water and a sponge (for moistening the tape).
Defend your prepared materials against a cat! (Apply only if you own a cat. If not, skip this step :) )
4. StepFill the tub or the tray with water and soak the paper in. Different papers take different times to soak entirely - it depends on their weight, material, etc. Also, warm water soaks in faster, so you probably want to experiment a bit. I think you're always safe with cold water, though.
The paper I am using (Arches hot pressed 300 lb) doesn't like long soaking, so I usually leave it submerged for five minutes in cold water.
(If you overdo the soaking, your paper could lose its sizing and wouldn't behave properly when used for painting.)
Take your paper out of the tub (or a tray), carefully hold it only by a tip and let drip off water.
Then lay it down on your board and with a tissue wipe off excessive moisture from the edges where you want to stick down the tape.
With your sponge moisten the tape and stick it down on the paper. Make sure you get out all the air bubbles and run your finger nail along the edge of the paper. Repeat the same procedure with all of the sides of the paper (it usually takes four times) :D
Now you are basically done and the waiting begins. It usually takes a few hours for a paper to dry, but it can be longer (again, weight and material come in play). You know your paper is dry when it doesn't feel cold to the touch anymore.
The paper may buckle while drying but don't worry, it will become flat again and you can paint on it without worries. The buckling is a sign that the paper could use longer soaking, though, so you may leave it in the water a bit longer next time.
I hope this will prove useful to you :)