A smoke detector could potentially start beeping for a few different reasons. For starters, there may actually be smoke or a fire in your home. The beeping is designed to warn you of this fact. If there isn't, the unit's internal battery could be dying. For whatever the reason, you can turn off the high-pitched, loud beeping sound on your smoke detector in just a couple of minutes.
Check your home to verify that it is not, in fact, on fire. Look in the areas around the smoke detector to check for flames. If the room appears hazy, also check any nearby kitchens or food preparation areas to make sure that smoke from cooking isn't tripping the smoke detector. Only proceed to "Step 2" if you are positive your home is not on fire.
Press the "Reset" button, if applicable. Certain smoke detectors have a "Reset" button on the unit's circular case, and pressing this button will stop the beeping noise automatically.
Remove the cover to your smoke detector. This is typically accomplished by rotating the cover until it comes off the base, similar to the way you would use your fingers to rotate a screw out of its hole. The cover will most likely have instructions to turn the case in a specific direction to detach the detector from the base.
Replace the battery in your smoke detector. Oftentimes if a smoke detector battery is about to die, the unit will beep to alert the user. Replace the battery and put the cover back on to get the beeping sound to stop.