Some years ago I met a friend for lunch just after she had picked her daughter up from her swimming lesson. Both of them looked ashen. Her daughter was about 5 at the time and apparently had just been on the sharp end of some “deep end learning”. Literally. This teacher had thought the best way to teach a child to swim was to make it a “sink or swim” choice. She worked on the basis that most children will swim for their own survival, and if they did sink, she would scoop them out.

Brutal. And needless to say, my friend never went back there.

It seems as though a lot of people become swimming instructors in the informal way: ie. place ads and hang a sign on the door.

This is a very dangerous way to go about things. It is so important to know who you are entrusting your child to, especially where water is involved. Aside from checking on their credentials, you will need to be sure that the pool itself is well maintained, etc. Here are some questions to ask:

Be sure to choose a qualified instructor. The instructor should be a member of at least one of the following organizations: US Swim School Association, World Aquatic Babies & Children's Network, American Swim Coaches Association, and/or United States Swimming. If you live outside of the US, you can find out if there is a swim school association.
Ensure that the instructor has knowledge of children and the approaches needed. The instructor must be able to take a "child-centered" approach vs. a task oriented approach.
Check that the instructor is knowledgeable and can help the child improve skills, but more importantly, positively reinforces things the child does well. Positive reinforcement will give the child confidence to improve and make corrections.
Check the pool quality. If your child is under the age of 3, the instructor uses a pool with a minimum water temperature of 87 degrees. If the child is between 3 & 5, the water temperature should be at least 85 degrees, and if the child is between 6 & 12, the water should be at least 83 degrees for swimming instruction. Competitive swimmers (usually age 6 and over) can practice in water as cool as 78 degrees (although 80 - 82 is ideal) because they are working harder, getting their heart rate up, and will actually even sweat in the water from the intensity of the workout.
Ask about the lesson details. The instructor should use Lesson Plans.

Be sure that the ratios are suitable. The instructor should promise a particular teacher; student ratio. Here are some excellent guidelines:

6 - 36 months: Parent & Me format, up to 6:1 ratio is okay since parent is in the water.
3 - 4 year olds: No more than a 4:1 ratio if a buoyancy device is being used. Without a buoyancy device, no more than a 2:1 ratio.
5 - 6 year olds: Up to 6:1 ratio if a buoyancy device is being used. No more than 4:1 ration if no buoyancy device.
7 - 12 year olds: Up to 8:1 ratio if the children can stand and/or have a buoyancy device.
Only agree if you can participate too. The instructor should allow you to watch every second of the class! If the instructor says you can't watch, you need to find another program. Never leave your child alone with anyone. Also, you are an extra set of eyes making sure your child is safe in the water. Constant supervision is one critical aspect of drowning prevention.
Seek an instructor of responsible age. In general, you would want a teacher who is at least 18 years of age (there are exceptions).
Do your research before payment. If the instructor has a "no refunds" policy, you better do some extensive observation of the instructor before hiring him/her. Find out what they will do if you miss class due to illness. If a make-up isn't offered, a credit for a future class is a good option.
Make sure the water is tested regularly for appropriate chlorine and PH levels. No chlorine is your biggest concern, and low PH will actually cause the eyes to get sore. Tip: You can buy a test kit at stores supplying pool equipment (box stores, sports stores, hardware stores, etc.) and test the water yourself.
This may qualify as helicopter parenting but if your child comes home with bloodshot eyes or rashes you would be within your rights to ask about this.

Teach. Watch. Protect.