Here is a description of how a Lemmings game works.  At the beginning, an entrance opens with a cheery Lets Go! from the as-yet-unseen lemmings.  The lemmings begin to drop from the entrance. When they hit the ground, they start walking.  At first, all of the lemmings walk towards the right-hand side of the screen.  When they are blocked by something, though, they turn around and walk the other way.  They would continue to walk until time ran out except for two things: first, they might fall into the sea, fall off a cliff, run into a trap or any one of a number of things which cause their premature demise.  Second, they might be changed from simple walking lemmings to something far more useful.  That is how you help the lemmings in their quest to get out - by causing them to take actions which will help them over the obstacles in their path.  You cause them to build a safe path from their entrance point to the exit, and once you have done that, the rest, as they say, is simple.

How to make lemmings do things

The first step in causing your lemmings to do something other than just mill about is to decide just what you want them to do.  You have a few different choices, and to select one, just click on the appropriate icon on the Icon Bar:
 

 Climber
 Floater
 Bomber
 Blocker
 Builder
 Basher
 Miner
 Digger

Next, pick a lemming to give the skill to.  You do this by moving the cursor over the lemmings on the game screen.  When the cursor is over a lemming, it will change from a cross to a box.  At that point, if you click the left mouse button, the skill you have selected will be assigned to the lemming who is under the cursor.  Note that there is only a limited number of skills available. Each time you assign a skill to a lemming, the count for that particular skill will go down by one - and when it reaches zero, you will not be able to use that skill any more.  Be frugal with your lemmings skills - as one of the levels says, Careless Clicking Costs Lives!