I know it seems overwhelming at first, but it's really not.
I presume you've read through the insert on how to mix the vaccine, right? Be aware you don't have to have the large bottle of sterile adjutent cold, just the small bottle with the wafer needs to be kept in the fridge.
Follow the directions for mixing the vaccine. I use one new needle/syringe for about every three or four chicks.
Get someone to help you. You'll want two boxes with paper towel on the bottom. One for the unvaccinated chicks, another to put them into once you've vaccinated them. Clear off a spot on a table, and lay out a towel or some paper towel.
Pull a chick out and have your helper help you hold it. Point its head away from you, cupping it with your hand. Lift the skin on the back of its neck up and away from the body, pinching it between your fingers to make a fold. Fill a syringe, then gently insert the syringe into the top of the fold (but not all the way through!)
You'll feel the vaccine make a slight bump under the skin as you're doing it. Easy peasy!
A good way to practice making subcutaneous injections is to get some oranges and some Hawaiian Punch (the red stuff.) Practice injecting the HP into the skin of the orange, but not too far, so it only goes into the white part, not the flesh of the orange itself. To check your work, cut the orange in half to see where the color of the HP went (we do this with 4-H kids to teach them to do Subcute versus IM injections.)
Hope this helps, and if you get desperate, email me offline and I'll send you my phone number, be happy to walk you through it when you're actually doing it.