Early troubleshooting coming up:

1. Provide us with the last three letters and numbers of your serial number. You can find it in System Profiler, Hardware menu, printed on the back of your laptop (or behind the battery), or surely on the box it was shipped in. That'll help us gauge what machine you're speaking of
2. Try charging the Macbook with a new power brick. You don't have to buy one... yet. Just ask a friend to let him borrow yours for a couple of hours, or drop into an Apple Store telling you suspect your power cord is broken, you'd like to get it checked and if it works you'll drop there to buy one later (which you actually should do)
3. If your Macbook doesn't charge with the new power cord, try with an SMC and PRAM reset. It's different between the Macbook with a removable battery and the ones without, so we may need your Serial Number to give you detailed instruction. If it still doesn't, go into System Profiler and tell us which data your Macbook gives about the battery
4. If the battery is fine, and the Macbook still doesn't charge with a new Power Cord, go check the Magsafe connector.
5. If your Macbook charges with a new Power Cord, you need a new power cord. That may seem rude on my behalf, but it isn't. There are many guides online that tell how to fix a Power Adapter with a stripped/damaged cable, but they're not worth it. Apple changes for free Magsafe with heat-damaged Magsafe Connectors, and if the damage is anywhere else, a patch-up job is likely to damage your laptop (think at a cut up cable badly patched with duct tape if it gets even slightly wet, or a power adapter not working as it should do). So assess if the connector is damaged. If it is, and fits the "Heat damage" description, bring it to Apple and have it checked to assess if it still fits the replacement program. If not, buy another one. There are economic spares from other brands, but I suggest to get the original, licensed one from Apple. iFixit itself and other sites sells them cheap enough.