How should I index a UUID in Postgres?
Use PostgreSQL's built-in uuid data type, and create a regular b-tree index on it.

There is no need to do anything special. This will result in an optimal index, and will also store the uuid field in as compact a form as is currently practical.

(Hash indexes in PostgreSQL prior to version 10 were not crash-safe and were really a historical relic that tended to perform no better than a b-tree anyway. Avoid them. On PostgreSQL 10 they've been made crash-safe and had some performance improvements made so you may wish to consider them.)

If for some reason you could not use the uuid type, you would generally create a b-tree on the text representation or, preferably, a bytea representation of the uuid.