How is it used to diagnose tooth vitality? What does the endodontist do?

The electric pulp tester is placed on the tooth to be tested, along with a drop of conducting paste. Then the tester is set at the lowest setting an a button pushed. Generally there will be no response. Then the dial is turned up a little & the test repeated. Eventually a little buzz is felt in the tooth & the patient signals to the dentist. The lowest level of response is then recorded. Generally the test is then repeated on teeth on each side of the tooth & often on corresponding tooth on the other side. Then the results r interpreted.
No response from the tooth generally indicates the tooth has died & needs the root canal therapy (or removal). A very quick response compared to the adjacent teeth generally indicates that the tooth is inflamed & probably is heading toward pulp death. If it responds the same as the other teeth then it is considered to be healthy.
The endodontist generally anaesthetizes the tooth & then a rubber dam is placed to isolate the tooth & keep mouth fluids from contaminating the inside of the tooth.
Then an opening is made into the tooth & small files r used to remove the remaining pulp tissue & to smooth & clean the canal. The canal is regularly irrigated, usually with a dilute bleach solution, which cleans out the filing chips & also to sterilize the interior of the tooth.
When the canal is clean & smooth down to the tip of the root then the canal is filled usually with gutta percha, a rubber-like material & a sealer. Later a final filling may be placed in the opening of the tooth, or it will probably be suggested that a crown be placed on the tooth if there was a pre-existing filling.
The filing of the tooth has been compared to having someone file on a piece of wood held in ur tooth, no pain, but often some vibrations.
Root canal therapy should be painless & most endodontists & dentists (your general practise dentist can also do root canal therapy if s/he desires & feel they have the skill) will not proceed until adequate anaesthesia is obtained.