I was wondering if anyone can find an electronic version of the Lemmings 3 manual.  If not, at least a brief overview of how the game works.

I guess eventually I'll figure everything out (after all, that's how I went thru Lemmings 2), but help is appreciated too.  Thanks.

I'ven't either, but I'll say that the main confusion is the "pick-up skills": when a Lemming picks up a skill, you can click on them while the "pick-up skill" skillbar button is pressed to use this skill.
Also, one of the skillbar buttons is "turn around", I think it's the first one.
Another is jump, I believe...

I don't know of any electronic version of the game manual.  I do have the game, though, so I can provide some of the important details:

General
Lemmings 3 consists of three tribes, with 30 levels in each tribe.  In each tribe, you start with 20 lemmings.  On a given level, only 10 lemmings will come out of the hatch, and the rest are kept in reserve.  These reserve lemmings come out of the entrance hatch to replace any lemmings that die in the level.  On some levels, there are extra lemmings that appear (usually, they are trapped somewhere).  Try to rescue these, too.  You need to have 50 lemmings from a given tribe at the end of the 30th level in order to complete the tribe.  To beat the game, you must complete all three tribes.  It is possible to save every lemming on every level.

The Skills
There are only five skills in Lemmings 3, and they are unlimited (you can use as many of them as you want).

1. Walker: The lemming stops whatever he is doing and starts walking.  If he was already walking to begin with, he turns around.
2. Blocker: The same skill as in the original Lemmings, only now you can free a blocker with the Walker skill.
3. Jumper: The lemming will take a short jump.  This is useful for clearing small gaps or getting past traps.  You can also jump over blockers.
4. Use: Makes the lemming use whatever tool he is carrying.
5: Drop: Makes the lemming drop whatever tool he is carrying.

The Tools
These allow the lemmings to build, bash, etc.  There are only a limited number of these, and they are generally scattered throughout the level.  A lemming can only hold onto one type of tool at a time.

1. Suckers: Allows the lemming to climb up vertical walls.
2. Shimmies: Allows the lemming to walk across the ceiling.
3. Bomb: The lemming drops a bomb at his feet and walks away.  The bomb goes off, killing anything nearby and leaving a crater in the ground.
4. Grenades: A lemming throws a grenade in the air.  It will bounce around for a while before exploding.  It has generally the same effect as the bomb.
5. Spade: Allows the lemming to dig through walls.  You can choose the direction in which you want him to go.
6. Bag of bricks: The lemming will build a bridge in the direction you specify.
7. Hadoken: The lemming will shoot out a hadoken, killing any bad guys in its path.
8. Umbrella: Allows a lemming to float down long drops.  The lemming will use this automatically when he reaches a big drop-off.
9. Swimmer: A lemming holding this tool will be able to swim the next time he goes in the water.
10. Clock: Adds a minute to the timer.

Creatures
The first three of these are bad guys, but the last one is actually useful.

1. Potato Beast: Walks across the floor, killing any lemming he runs into.
2. Psycho Buzzard: Flies through the air, and occasionally swoops down to pick up lemmings.  He also tends to sit and wait for a lemming to walk by.
3. Lemme Fatale: I don’t know exactly what this one does.  It generally does not become much of a factor in the game.
4. Mole:  This creature can be used to dig though the ground.  He will start digging when he hits bricks or steel.  Once he is digging, he will bounce off of any bricks or steel he runs into.  He will stop when he runs out of material to dig through.