Sometimes tragedy strikes and a treasured pot throws itself on the floor or suffers some terrible blow.
If you want to redeem the situation and make your pot whole again there are a number of options...
* Simple DIY
Use a 2 part epoxy resin adhesive (eg Araldite in the UK) and carefully follow the instructions.
* Advanced DIY: Kintsugi
This is a traditional Japanese technique using lacquer and gold to re-join the break and celebrate the repaired character of the pot, so it is associated with the philosophy of wabi-sabi. It's a detailed and skilled process that can be slow as many layers of lacquer have to dry before the next can be applied, but the results are I think beautiful. If you'd like to try a basic version you can buy kits online.
* Professional restoration/conservation
There are numerous professional restorers/conservators who can do the repairs for you. I can't recommend anyone in particular, but they should all be trained and prepared to show you a portfolio to help you decide who to use and what type of repair to commission. Try this list of ceramics specialists as a starting point. Restorers will do an 'invisible' mend, conservators take a museum-type approach of making the joins reversible and evident so than you can see the history of the pot.
Alternately, if it's a bad break and not a valuable piece you might like to try some mosaic!