The honest answer to your question is "have you got all day?!!" But briefly:
The aircraft has a Flight Management Computer within which can be programmed, or stored, the route you are about to fly. After take-off if LNAV (Lateral NAVigation mode is engaged, the aircraft will follow that route until the pilot intervenes by selecting another mode - such as Heading (at a command from ATC for instance) or Approach Mode (to follow the ILS). There are lots of little subtleties - such as when the ATC controller gets you to fly headings to route you clear of other traffic, then clears you to route direct to another waypoint, you can programme in the direct track, re-engage LNAV - and again, the aircraft will go direct to that point.
Routes flown are not just 'lateral' though - there are altitude and speed constraints (limits, if you like) to be met at various points on the route and VNAV (Vertical NAVigation mode) is provided to cater for this. Put simply if, say, a standard arrival route requires you to be at a certain point at a certain speed and altitude - then VNAV will put you there by governing the aircraft's vertical profile. Again, there is a lot more to it than this! For instance, VNAV governs the engine thrust, speed, Mach Number etc .. and will attempt to fly in the most economical fashion - telling you the optimum flight level as well. There's lots to it, and training courses devote a lot of time to these features, so a few lines here only scratch the surface, I'm afraid - but I hope it gives you some idea.
Can't help you with the DC10, though - my experience of that aircraft is confined to sipping a libation in the back as Greenland rolls past the window!