I'm a moron with a simple problem (I think)
 

I'm a newbie and recently took to commuting with a ten year old bicycle. I wiped out on my first ride home from work. During the wipeout, the brake levers mounted on my handlebars became loose. I cannot for the life of me figure out how to tighten these Shimano levers on my handlebars; there's no apparent screw to tighten. What is this moron missing? How do I tighten these things? Thanks in advance for your help.

Are they just brake levers or "brifters" (combined brake and shifters)?

For brake levers, pull on the brake lever and you will see a bolt inside that clamps the lever to the bars. Newer levers require a 5 mm allen wrench and the older ones need a flat blade screwdriver. The brake cable may be in the way so you will have to loosen it to get to the bolt.

If they are Shimano brifters, there is a groove along the outside face of each lever that disappears under the rubber hood. At the base of this groove is a 5 mm allen bolt. Slide an allen key under the hood following the groove until you locate the bolt. Clockwise to tighten and counterclockwise to loosen.

just brake levers. I'm headed to fix this now. Thank you.

any pictures?

Thank you. I've got the levers tightened.

They should be tightened enough to stay put with you hands on them going over bumps. But not so much that they won't "give" if you get into an accident. They were, it seems, properly installed as they gave way when you impacted. Too tight - they may well break.

Happy Trails!

Thank you guys for the advice. The brake levers are tightened appropriately. I've also installed new tires. Thank you.