In the photograph I'm discussing a point during a demonstration, and using 300lb paper held to the board with two clips, as it is essential to keep the paper firmly in position. In the studio I normally use stretched 140lb paper. Firstly I cut four strips of gummed tape to correspond in length with the edges of the paper. Then I immerse the paper completely in water for not more than 15 to 20 seconds. If you leave it in water too long there is a danger that it will tear the tape away from the board. I then hold the paper by one corner and allow the water to drain off before laying it flat on the drawing board, before wetting each gummed strip in turn and sticking it down over one edge of the paper. Finally I lay the board flat and leave it to dry out completely before using it.
Every art tutor will give you a different formula for stretching paper, and if one method doesn't work for you after several attempts then try someone else's recipe. Alternatively you can buy stretchers for the purpose, but you are then limited to certain sizes, and if like me you have many boards stretched at once this may not be to your liking. Depending on the amount of water you use, as well as the paper itself, you may find it still cockling with really fluid washes, even though you have stretched it well. Some papers are more prone to this, but good paper like Waterford, Bockingford and Fabriano should not give you any problems. Worst of all, perhaps, is de Wint tinted paper, which can rise up to half an inch off the board, even after stretching. However, you won't have any problems with it, as it's no longer available! Further advice on stretching can be found in my Watercolour Landscape Course book, which is available on my website.