I'm going to guide you through the steps you need to take a really cheap battery-operated alarm clock and make it much much quieter.
A plastic alarm clock run by a AA battery.
A very small screwdriver that fits into the screws that hold the clock's case together. Probably a very small Philips-head screwdriver.
A small slotted screwdriver.
Lightweight oil, like 3-in-1 oil, sewing-machine oil, or watch oil.
You may need a pair of pliers - jeweler's pliers are nice.
A quiet place to work where you won't lose the little parts.
What we're going to do is take the clock apart, put a drop of light oil on the parts that clatter every second, and put it back together. The oil should keep it quiet for quite some time. Maybe as long as you can expect these cheap little clocks to last.
First, pull the knobs off the back of the clock. They're probably held on by friction or by tiny springy plastic "arms" visible in the little hole in the knob. You may need to push the plastic parts together with a screwdriver or pliers - or you may be able to just pull the knobs off.
Did I remember to take the battery out? Take the battery out. Now you can unscrew the little screws that hold the case together.
Be careful now. There are thin wires soldered to parts on both sides of the case. Don't yank on them, or you'll have to solder them back when they pull off. And there's a little coil of copper wire - very very thin. If you even think about touching that, your brain waves will break the wires, and you won't be able to fix it.
The clock movement is the plastic module with wires going into it. We're going to take the back of the movement off. It's held on by clips molded into the plastic. Mine has two kinds of clips. One kind is sprung by pushing the black clip away from the clear top.
The other kind is sprung by pulling the clear clip off the black back. They're all brittle. If they break, you're probably still going to be able to put your clock back together, but be careful.
Unclip all the clips, carefully, and then pull the clear top off.
Here's the movement with the back off. Don't touch those copper wires.
There are little dimples in the inside of the clear piece. They're bearings for the gears. Now put a tiny drop of oil on each of those dimples.
On my clock, there's a gear that comes off first - you can see it sitting on the table in back of the clock here. There's a tiny gear attached to a tiny magnet that's revealed by this - I'm holding it in needle pliers in this picture. Lift it out, don't touch the copper wires that are nearby.
Where that tiny gear with the magnet was sitting - there's a little bearing hole that the gear sits in. Put a drop of oil in there. This is the place where the oil really helps quiet down the clock. Now put that gear back where it was.
While we're here, put a drop of oil on the teeth of that gear.
Put the remaining gear back into place and snap the cover back on the movement. Now close the clock up carefully - make sure you don't pinch the wires. Make sure the snooze button (if it has one) is back in place. And reattach the screws and knobs. You're done!
Did you put the battery in?