There are 2 basic syringe types; One where the needle screws onto the syringe and the other the needle slips onto the syringe..
I prefer the screw on type called a "Luer Lock" syringe, less chance of the needle coming off while administering medication.

• Luer-lock, which locks the needle onto the nozzle of the syringe.
• Slip tip or Luer Slip, which secures the needle by compressing the hub onto the syringe nozzle.

This shows the parts of a Luer Slip Syringe used for giving injections

• Always use a clean needle and syringe
• Wash your hands with antiseptic soap before handling the needle and syringe.
• Check the label on the vaccination or medication bottle to verify it is in fact the one you want to give your goat. Double-check the expiration date, make sure there is nothing floating in the bottle and that the drug is not discolored.
• Wipe top of medication bottle with alcohol prep
• Use separate needle for drawing medication from bottle so as not to contaminate medication- to do this  if you are using a syringe and needle combo, unscrew the needle on the syringe, and screw the syringe into the needle that is already in the rubber stopper of the medication (One that you have already placed there for this purpose) - once the syringe has the proper dosage of medication in it, unscrew the needle that is In the medication bottle and re-screw the needle you removed before  filling the syringe back onto the syringe.
• Make sure injection needle is properly attached to syringe (With a luer-lock syringe the needle will screw into  the hub of the syringe , then while holding syringe upside down needle pointing upwards.. loosely in one hand.. flick with your fingers the top of the syringe to get air bubbles up to top, then expel them by pushing plunger some until you are to pure medication.
• Secure goat either in a stancheon or using a collar or second person and secure to a fence , tree or have the person hold the goat securely  if you  cannot hold the goat and give the injection.  It helps to have the butt end of the goat up against something solid so they cannot back away which is what they typically do.
• Wipe injection site with alcohol prep, double check dose amount in syringe and double check the medicaiton to make sure you in fact have the correct med.
• Remove the needle's plastic, protective cap. Be very careful not to touch the needle.
• Insert injection needle into goat at what ever angle you intend on giving injection (Sub-Q or IM) - SQ goes in at an angle , IM goes straight in.
• Draw back on plunger to make sure you are NOT in a blood vessel! (This is especially important for giving penicillin injections as Penicillin is deadly if injected into the bloodstream)If you are in the vessel ..withdraw needle and re stick the goat.
• Slowly and firmly inject medication (if the goat moves and you think there is a possibility of breaking the needle- Let go of it and let it hang.. you do much less damage with the needle hanging there than trying to hold on and taking a chance of breaking it off in the goat!)
• Withdraw needle and rub injection site briskly.
• Let go of goat and apologize for giving it an owie. Give her a kiss and a cookie.
• Watch her for at least 30 minutes.. this is why I bring mine inside if at all possible. Keep an eye on her the next few hours Just in case..