Decide what length and gauge needle you will need, and locate one.
Make sure you have positive pressure in the vessel you are syringing from. If the experiment is air- and moisture-sensitive, (i.e. the vessel cannot be open to the air), attach a balloon or an argon line. If you are using a Sure-Seal bottle, especially one that was refrigerated, release any pressure that has built up within by attaching a balloon.
Clamp your bottle or flask firmly.
Make sure pressure can be released from the vessel you plan to syringe liquid into. Options include
An argon or nitrogen line
for experiments that are not sensitive, sticking a disposable needle through the septum is sometimes convenient.
Pull the liquid into the syringe, taking slightly MORE than you need for your experiment.
Tip: Keep a good grip on BOTH the needle and the plunger. Built-up pressure can send the plunger and a lot of liquid flying, and needles not secured by Luerlock fall off syringes easily.
Flip the syringe needle-up, so that air/inert gas bubbles rise to the top. For dangerous liquids, it is best to keep the needle tip stuck in the bottle. If you use a long needle, this is easy to do. Tap the syringe a couple of times like you've seen doctors do in the movies, and look to make sure all the air/gas has been collected.
Use the plunger to remove the air/gas, and adjust the amount of liquid in the syringe to the exact amount you need.
Now that you know exactly how much liquid is in the syringe, tip the needle up again and draw a small layer of gas (air or argon) into the syringe. This keeps you from spilling and if necessary, protects the liquid from exposure to air during transfer.
If you had the needle in a bottle all this time, you can remove it now, keeping the air layer at the syringe tip.
Insert the syringe into the destination septum, keeping the air layer between the syringe and needle (you need a long needle for this), and then flip the syringe over. Holding the plunger down, inject the air/nitrogen cushion in your reaction first, then continue to inject your liquid into the flask (dropwise if needed). After complete addition, pull back the plunger and remove some nitrogen into the syringe (keeping the syringe tip pointing up at all times). There will be a small amount of excess reagent in your syringe. (contributed by Alex Hird)
Note: The syringe volume markings do not take the volume of the needle into account- this is usually not an issue, but is an important detail to remember.
Clean the syringe and needle immediately by flushing it with solvent. Choice of solvent will depend on the reagent:
For inert reagents, use acetone.
For alkyllithiums, use hexane (this dilutes the reagent), and carefully add the hexane washes to ethyl acetate. Flush the syringe and needle with this mixture a couple of times, and then wash both as usual with acetone (or toss the disposable syringe).
For Grignard reagents, use ether for flushing, and use the procedure above.
For other reactive reagents, use the principles described above, and good judgment.