The most common techniques are:
1) Get it done by someone else with skilz and machines beyond your own
2) the "rails" method where rails with screw holes are placed aside the barrel as it sits in the stock, screwed down to follow the taper, and then the side walls of the barrel channel are cut in to the minimum depth. Chisels, gouges, scrapers.
3) the freehand method- scribe the sides of the channel, gouge out or plane out the center to get the bulk of wood out, then use chisels, gouges and scrapers.
4) The hand saw method- after scribing the sides of the barrel channel, use a saw with the kerf removed to cut the sides of the inlet, with or w/o rails, then chisels, gouges, scrapers
5) the router method, of which I know nothing. Sorry, I know that's what you asked for.