...a broken pot? You can't, not really. But you can mend a cracked pot (as opposed to a crackpot, which there's no real fix for, either.) I recently learned a way to mend cracked greenware and leatherhard ware. One of my students came back from a workshop with a method that has worked for her, so far: paper clay.
Tear up tissue paper into small shreds.
Add a little water to make a "mashed potato' consistency.
Add about 2/3 as much thick slurry, of the same claybody as the pot you are trying to mend.
Apply thickly to the cracked area.
Remove most of the slurry, but leave enough to the crack is totally filled.
Let dry ever-so-slowly. I have a leatherhard pot pictured here but I am told it fixes bone dry ware as well. If you've tried it, give me a shout -- I'd love to have verification.
And, I am delighted to say I invented a repair for cracked bisqueware!!! I fill a glaze pen with a high-clay-content shino, and completely fill in the crack; and then glaze over it with something other than shino. I have successfully mended BIG cracks this way. I think the shino stretches as the crack expands in the firing, so the fix holds.