After scaling the side of the seat, go ahead and move it into the second quadrant with the top and bottom of the seat.
Select the side of the seat, and move it just over the circles. But not too close if you want to select them again to move them in the future.
Texturing tip: If you want good textures, it is important for your uv's to be consistent in size. For this example, the side of the seat has to be close to the same size as the top and bottom of the seat. In other words, if you were to wrap the side around the circle it should be long enough to wrap all the way around. You may have to stretch the length of the side piece. This will keep the texture looking consistent among the whole model.
Now that the seat is layed out, we're going to move on to the legs of the stool. Go back to object mode by hitting F8 on your keyboard. Select one of the legs of the stool.
Hit F8 again to go to component mode, and switch to the Face option and select the entire leg.
Just like the side of the seat, select the Cylindrical Mapping option.
For the most, this does the trick but there needs to be some tweeking with cylindrical tool.
Notice at the bottom of the cylindrical tools there is a red "T" shaped tool.
Click on the bottom of the red "T".
If you look in the uv texture editor, you will see that the uv's for the side are now projected and layed out
Notice that at the center of the cylinder tool there is a blue circle that shows up.
Click on the blue circle.
Notice now that you have all of your rotation tools available. Rotate the cylindrical projection so that it is parallel to the leg. If you are doing this as you look at the uv texture editor, you will see a real-time change in the projection. The goal is to get a uniform box of squares for the projection. This will ensure the least amount of stretching for your textures.
Doing this and getting it right takes quite a bit of practice and time. Don't get frustrated if you can't seem to get it to look just like this image