I' not a hand feeder or breeder, and I'm not necessarily sure there is a right way to hand feed chicks. I have heard of people inserting the syringe on either side of the chicks mouth without problems, and one hand feeder even inserting the syringed from the front of the mouth and never having deformed beaks. Their reasoning for feeding that way is because of the way the parents would naturally feed the chicks.
Casey, my cockatiel, was hand raised from day one, but I didn't get her until she was 5 months old. Well, I didn't know about her until she was already home! Of my other birds that were hand raised, I don't know how they were raised at all.
Generally speaking, it's recommended to leave the chicks with the parents for a minimum of 2-3 weeks. Hand feeding day one chicks is *NOT* an easy task and requires feeding around the clock every 2-3 hours. You wont be getting any sleep. It's easier for chicks to digest formula than it is to digest whatever food the parents have been eating, so formula goes through their digestive track a lot faster. If left with their parents, it helps them get some beneficial bacteria into their systems which can help keep them healthy.
Some thing you need to worry about when hand feeding....
*Crop burn
*Overfeeding
*Underfeeding (and consequently, overstretched crop)
*Slow crop
*Sour crop
*Yeast infections
*Aspiration
*Crop impaction
*Cold chicks
*Overheated chicks
*Dehydrated chicks
etc
IMO, hand feeding is extremely easy to do! And it makes mistakes that much easier to do!
I've heard of a story of a man who bought an unweaned chick and was told to check the temperature of the formula by putting it on his wrist. The guy had *NO* feeling in his wrist, and burned the crop of his chick. A burned crop can easily break open and food will leak out of the crop.
Another man thought "hand feeding" meant feeding chicks seeds by hand. He had an unweaned baby that didn't know how to eat seeds just yet...
If you are squeamish, please don't view these links. If you can handle it... here are photos of hand feeding gone wrong as well as photos of chicks in distress. (various ailments and issues that arise)
crop burn damage
Babies In Trouble Photos by Mousebirds-and-more | Photobucket