First off, getting a babysitter you can trust can be quite a task in itself, here are some places you might find leads on a babysitter.
Your local Pediatrician, dentist, or allergist office
Local church or place of worship
Your local health department
Mom and Parent Groups on Facebook
Word of Mouth recommendations from other parents
Civic or Volunteer Organizations you belong to
Online resources such as care.com or sittercity.com
Your gym or yoga class
Local schools and teachers you trust
Keep in mind, no matter where you get the lead, make sure you personally interview each potential care giver and feel really good about the decision. If you have doubt, then you should probably listen to your gut.
Secondly, when you do decide on a sitter, are they prepared in case of an emergency?
Do they have an special training such as CPR, and if so, do they know how to perform on an infant or young child?
If you have a household pet, are they comfortable with animals?
Here is a checklist many parents find helpful:
(To be left with sitter)
Names of parents, home address and phone numbers
Emergency numbers for your area (911/police/fire department/poison control)
Names and phone numbers for your pediatrician, hospital and alternative contacts
Names and phone numbers of neighbors
Special Instructions for your child such as: normal routine for meals, bath, and bedtime, medication instructions, especially if a food allergy is involved
List of your child's favorite toys or activities such as their favorite book to read or game to play
Some other things to consider....
Before you leave your sitter alone with your small child, make sure your babysitter feels comfortable with your home, give him or her a thorough tour. In doing this, you can make sure they know where all the first aid supplies are located, as well as the phones, exits and potential problem areas like a room that is "off limits" etc.
But above all things, make sure you as the parent and your sitter are comfortable, both parties need to be at ease for your child to get the care they deserve.