Step 1: Materials/Tools
An empty tube of caulk/filler/sealant, a long stick and a hacksaw. Chop off the end with the hole in it about one centimetre down (this will be the needle end of the syringe) and poke out the internal bung with the stick (this will be the blunt end).
A plastic bottle (I used a two litre lemonade) and some sharp scissors. Cut the top and bottom off the bottle and roll it to fit the ends of the capsule. Add a layer of sellotape to hold it, and glue one end in place.
A caulking gun (presumably you'll have one around, if not then they're a few pounds at a DIY store).
A clear plastic straw and a bolt (optional but I think it looks quite nice). Cut the end of the straw at a slight angle with the scissors and screw it into the bolt if youre using one.
Step 2: Constructing the capsule
You'll want one end to be removable to get the glow stick out later (unless you want to spend hours shaking it and hoping that it falls out, or you intend to gradually fill the capsule to the brim with old sticks).
Glue the bolt and straw to the needle end. The bolt makes it look more real to my eyes, and gives a larger surface for the glue to hold on.