Oh I forgot: there is no helpscreen yet, so I'll explain the keys here:
Shoulder buttons: zoom in/out
Nubs: panning
dpad: steer the current selection of lemmings
Touch: nearly everything else
F: Faster (or click the "+")
S: Slower (or click the "-")
action button A: select all lemmings
action button X: explode
Exit level: Q or SELECT
Exit game: ESC
There are 6 actions: select, build, dig, explode, climb and float. Not all levels have all actions available, of course.
The first three of those (select, build, dig) have big buttons and remain active once selected. The last three (explode, climb, float) have small buttons and can be assigned only once to a level. If you click the button, it will assign the skill to all lemmings in the current selection (initially all lemmings are selected), at least until you have no more of the skill.
The selection action is used to change the lemmings selection. You can just draw a rectangle on the screen, and all lemmings inside the rectangle will be selected.
The build action is used to make bridges and other structures. You can draw stuff on the screen (there are three different brush sizes you can use) and lemmings will try to build the corresponding structure by locking themselves into place. You'll have to get used to how exactly it works.
The dig action is used to dig tunnels and to unlock builder-lemmings. You can draw on the screen just like with the build action.
If by unlocking builder-lemmings, a bridge becomes suspended in mid air, it will fall down. This can be useful, because petrified builders cannot die from falling, so you can use falling bridges to survive big falls without needing floaters.
A normal lemming can climb two vertical pixels per horizontal pixel. So it can climb on top of another lemming. Climbers can climb straight up, but once they hit an overhang (i.e. there is a pixel right above them), they change direction and will probably fall down. However, if they hit a perfectly horizontal ceiling, they can cling to the ceiling without falling down.
Normal lemmings can survive a drop of less than 40 pixels (don't count too much on the exact number, it might still change). Floaters open their umbrella/parachute/glider/whatever after falling 20 pixels, and from then on, they fall at a somewhat random and slower rate. They float in a randomly changing direction, which can be controlled with the dpad.