What kind of bike is it? I'm assuming it's a mountain bike...
It's almost certainly a problem with the rear derailleur (the bit that the chain snakes through under the cogs at the back) or the shift lever that controls it. I'm assuming, if it was made in the last ten years or so, it'll have indexed shifting: the lever which changes gear "clicks" from one gear to the next (as opposed to friction shifting).
There's a spring in the rear derailleur which tries to pull the chain across the freewheel from left to right (ie from lower gears to higher ones) but there's a ratchet in the lever on the handle bars that prevents this from happening except when you want, in theory. These are connected by a cable, which should be JUST tight enough to be able to pull the derailleur all the way to the left when the shift lever is all the way round, and there's a pair of stopper screw to stop the derailleur moving too far towards the wheel, (or too far away from it). If you can't get into first gear, then the cable is too lose. you'll need to move the lever all the way round (to first), push the derailleur across with your hand til it hits the stopper, then get a friend (this needs a few hands) to loosen the nut holding the cable, pull it through as hard as possible, then tighten the nut again. (The nut will probably be a 6mm allen key type, but it may not be.) The problem SHOULD now be fixed. Check the other stopper on the deraileur won't let the chain move too far the OTHER way, away from the wheel.
If you CAN currently get into first gear, then the cable itself is tight enough, but the ratchet in the lever that pulls the cable to change gear isn't. To be honest i'm not exactly sure how they work (mine are a bit special, so they're different to most)—it may well just be an easily visible screw on the lever, but it shouldn't be tricky to figure out once you know where you're looking. If there is such a screw, a half turn clockwise may tighten it enough, possibly a little more but it won't need wild amounts of adjustment.
This may make no sense at all, but it's the best i can do at this time of day!
This picture may help a little: in particualr the "cable anchor bolt" and "limit adjusting screws"
