I've only used a pet sitter once and that was just a few weeks ago. I got some great ideas from people here as far as what to do/leave, so I'll pass those along:
--I did tell my regular vet that we would be gone, for how long, and the pet sitter's name. They made note of it in all my kitties' charts. They said that they would bill me for any charges but would call to let me know what was going on before doing treatment (unless it were a life-threatening emergency). The pet sitter would have called us, too, of course.
--I did not make this arrangement with the emergency vet, however. It is close to the house and the pet sitter knows where it is so I wasn't worried about her being able to find it or anything.
--I left my vet's name, address, and phone number for the pet sitter. I printed out directions from our house to the vet's office and left them on the table.
--I made an info sheet for each kitty. This was the best tip I got, and I'm sorry I don't remember who told me about it to give credit, although I think it was Hillary and also JJ. The info sheet included each kitty's name, age, weight, sex, and spayed/neutered status. I also put the vet's info as well as our info on it. It had a section for "Major Medical Issues", just as an overview. This is so that in a real emergency, the vet does not have to wade through the complete records of the kitty (which I also provided) to see the major events. These sections were pretty short because luckily my kitties have not had too much go on with them. I listed Buzz's like so: "July 2009 Buzz was diagnosed with diabetes. On 8/10/09, switched to canned food and began insulin treatment. Remission was achieved Dec. '09." Obviously if she were still on insulin I would list the type and how much she gets per day. I had a section which listed medications, and one that listed food. I also noted in 3 different places that she was NOT to receive steroids unless there are NO other options.
--I put the full medical records, the info sheet, and the directions to the vet into a manila folder, one for each kitty. This way if there were an emergency, the sitter could just grab kitty and envelope and hotfoot it to the vet.
The info sheet was more for the ER vet, because obviously our vet already has the records and knows what's going on. It definitely gave me peace of mind. I like Vic's idea about leaving cash for a cab if it's your neighbors who are pet sitting.