Old unit out through the same tight path it came in — utility closet, garage, or crawlspace access sets the pace of the whole job. New unit in: compact wall-hung or small floor-standing, sized to the heat loss. Near-boiler piping repiped to the new unit's requirements (primary-secondary on most modern installs), new circulator and controls, expansion tank sized to the system volume, and venting to code — which in a slab home usually means a sidewall vent, not the old chimney.
Then: fill, purge air from every baseboard run, verify cold pressure near 12–15 psi, fire and combustion-test, and confirm every zone actually heats. A good installer leaves you with the pressure reading, the combustion numbers, and the manual — not just a warm house. Plan for the house to be without heat during the workday; in winter, that takes scheduling, not luck.