You do not have to wait until the child is a certain age. Even though the first birthday is a milestone the earlier kid's haircuts are introduced the better. As long as the child can sit up by him or herself. However, if your child is more comfortable sitting with you then it can be allowed the first few times. Do not be afraid to leave the room if things get crazy, in some cases the child responds better if their parents are not in the room. It is very important to establish a solid relationship between child and stylist. It may be necessary to have the child tag a long on a couple of your own appointments in order for them to build trust with your stylist.
Never be overly picky on the first kid's haircut. The first haircut is more of an introduction than anything. Familiarize the child with the stylist, cape and tools. The goal should be to get him or her in the chair and diminish anxiety. Some stylist will worry too much about the temper tantrum than the task at hand so make sure you discuss this with them prior to the first appointment. Too much time spent consoling the child will only drag out the process and make the child lose patience. It is helpful to talk to the child for a few minutes and then get started. It takes a lot of patience for a kid's haircut so that is also something to discuss with your stylist, if you have a good relationship with him or her do not be afraid to come out and ask "Are you comfortable doing a kid's haircut?" If they are not they should be honest and say so and hopefully be able to refer you to someone that is.
Be consistent! Try to get them comfortable with the stylist. It is not a good idea to be a "salon hopper" when it comes to children. Trust is important. If you make standing appointments with a stylist consistently then why would you trust anyone else with your child? Some planning may be required but rather to have them with someone you both trust than to go into any salon just because it's Easter Sunday or some other special occasion. Some salons are even geared toward children and have special seating and different items all specifically designed for kids. Don't feel like you have to go to those places especially if your stylist has a good rapport with you and your family.
Children have the ability to reason and understand more than we know so don't be hesitant to "talk up" the haircut before it ever takes place. Letting them know that they are going to see miss stylist tomorrow so she can cut their hair is never a bad idea. If you chose to spring it on them sometimes they automatically go on the defensive and you may not even get them in the door especially if they have had a bad experience already. One very important thing to remember is the calmer you are the calmer they will be so try to keep your cool if possible. You do not have to scream and yell, however, once your child is in the chair if a temper tantrum ensues follow through! If you let them out of it at that point you've lost the battle, even if the stylist only wets the hair and combs it they have seen that they cannot just get angry and get out of it. This is more important for young children if your child is already five or six years old then of course they will know better so in that case actually doing the kid's haircut is necessary. Try to be encouraging and refrain from using phrases like "she'll cut your ears off!" Although it seems like a good idea at the time it will freak them out and make things worse. In some instances it actually works better if mom or dad leaves the room.
Always be encouraging even for the smallest steps. Let the child know he or she is doing well sitting by them self, wearing the cape, etc.) In some cases bribery is fine! Balloons, candy, stickers or anything else you choose is fine. You can also let them comb their own hair during and after. This allows them to feel like they "helped" with the haircut.
In closing I would like to emphasize these things again. Trust in your stylist is very important and trusting their skills with both you and your kid's haircut, also being consistent as with everything in parenting if you give up on it once they remember so it is the same for their haircuts. Finally, make sure to always praise the child for small steps. We all need encouragement from time to time especially if it may be an experience we are not sure of or may be a little frightened of.