Imperial Guardsmen, being led by an officer and his command squad
Where to begin when explaining the 40k tabletop game? Well, I suppose we can start with the most basic principles. 40k is a tabletop game - that's right, this game isn't played on a console or on your computer (well.. they made those after the fact). Rather, it is played on a large surface (somewhere in the magnitude of 6x4'). There is no "board". Each player possesses an army, and that army contains individual models; most are 28mm (1.1 inches), but there are also various vehicles [walkers, tanks, aircraft] and other types of units.
Before you play,
Before you get into the heat of battle you need to get your army ready. This typically includes purchasing the models from Games Workshop or from some 3rd party. You must then assemble them (most are plastic and come on "sprues" which you must cut the pieces out of - think gundam model box kits). Assembly requires nothing more than some super glue and a nail file for rough edges. After the models are assembled you need to paint them! Painting is great because it lets you give your army a unique feel - are they a stealth force dressed in mostly black, or from an old chapter whose color scheme is already set. Once they're painted and you decorate their base a bit (the base is the little circular piece of plastic they'e glued to - see the above picture) you're almost ready to battle.
A battle force of Ultramarine-chapter Space Marines are ready for battle!
Making an army list,
After you have your troops purchased, you need to make your army list. All units in 40k have point values. As such, players with two different armies can compete on an equal footing in say.. a 1500 point battle. Each "army" in the 40k universe comes with a codex - aka, army-specific rules. Armies range from the human Imperial Guard, to Orks (space orks~), Tyranids (think alien from AvP), eldar (space elves) and a bunch of others. The army codex contains various ways to customize your army and get it ready for play.
Find a friend, or local gaming store where 40k players gather, and play! Most competitive matches will include detailed terrain (miniature structures/bombed out ruins/trenches/bunkers) with which to do battle in. Ask for tips from your opponents on how to improve your army or check out various internet forums dedicated to the hobby.