The double-slit method is the way to go. You can easily get wood for your work by tearing down your constructions, as I assume you haven't been stupid enough to make blocks out of it (since you get one block per log, it IS stupid). You can the use 3 logs to make a screw pump (where you actually need a (wooden) block... only useful use of wooden blocks I know of), and then you use further recovered logs to shore up the walls. Note that the double slit method results in a lot of cancellations due to the water.
Because of that, I only have building enabled on my two miners, who also have mining and pump operating skills. This means one pumps and the other digs/builds, and you don't have to wait for someone half across the map to get to the building site because the bugger picked up the job before the miner did when the miner was interrupted.
You need 1 log for the carpentry shop, 3 for the screw pump, and 10 for each soil aquifer level (max 2 levels). Below that you'll have stone (if you're unlucky enough to have aquifer bearing rock you can switch to the smoothing method to block the aquifer, which is a lot faster, easier, and less subjected to cancellations.
If you've somehow used up all your logs on crafting, you'll have to wait or resort to the cave-in method.
For the double-slit method, read the instructions, follow them closely, reread,.... Once you think you've got the hang of it you'll probably screw up (at least I did). Also, when you realize that you've screwed up by forgetting to leave a sink on the 3:rd pass on the lowest level, don't panic, as it can be recovered, although at the cost of additional cancellation spam: Since you probably realized it when pumping out of the 4:th pass fills the other slit, stop pumping, turn the pump around, empty the filled slit and remove a wall segment to create a sink. Turn the pump around, process the 4:th pass as if it was the 3:rd, i.e. leave a sink. Turn the pump around again and plug the hole you made in the wall.
You can also use the Deployable Drain method to recover.
martinuzz is almost correct: a desert with a rainfall of less than, I think, 4 will have no saplings spawn, and less than 2 (I think, again) will have no shrubs spawn.