I perform a lot of very similar reactions myself. Best way I've found is to add the pyridine (dry) to the amine in freshly distilled THF under argon (or N2), and then add the acid chloride to this at 0°C drop wise. I think it's more common to do as wildfyr suggested and add the amine to the acid chloride, but I have never had any issue doing it the other way. I should note that cooling the reaction during this addition is very necessary; it heats up quite a lot and releases HCl gas.
You will want to have it under an Ar or N2 ballon rather than attached to any manifold as well. Once it's added, you can warm to room temperature or reflux. I generally let it go overnight and then quench with 1M HCl under argon.
If you are lucky, acid base work up will do the trick in terms of purification. I guess it depends on your amine. The amines I work with are not quite as nucleophilic, and I have to do a few other things in order to purify. Namely, I wash the residue with cold solvent (depends on the product, but often this works well with EtOAc) and then recrystallise the collected solid in whatever works (EtOAc and PS, usually).
One other thing: quality of your reagents is very important. Everything should be dry. I boosted my yields from ~20% to 80% just by distilling the chloroacetyl chloride I was using prior to the reaction (incidentally, one of the worst things I've ever had to distil).