As I embarked on wiring my COE, I felt a bit intimidated, as you apparently do. It turned out to be a very enjoyable process. In addition to the above suggestions, let me add;
1) First, disconnect both battery cables. Not a bad idea to remove the seat cushion before starting, as you will spend some time under the dash. Remove the gauge cluster and headlight switch from the dash, drop them down so you can access them easily (cluster will remain attached to the temperature capillary tube--don't break that!)then remove the original harness. No need to worry about the old wires, assuming your new harness is properly marked.
2) Start by threading the new harness through the firewall grommet, from the inside. It goes through the grommet easier than the other way or you will be pushing cluster light sockets through the hole. Turn your attention to the headlight switch and gauge cluster. Be sure you have connected the gas gauge correctly, you don't want to fry your gauge if you have reversed the wires. You should have a smaller ignition harness that goes through a separate grommet. Get that connected to the ignition switch and ammeter before replacing the switch. Note Steve H's suggestion to use the old dome light wire as a assist to get your new wire through the A pillar. The lights to the speedometer and wires to ignition switch can be be accessed adequately without removing them.
3) Go to work on the engine side of the firewall, attaching the proper wires to the voltage regulator, terminal blocks for the headlights, brake light switch, dimmer switch and horn.
4) Wire your tailight(s).
5) Before hooking up the battery, test the positive and negative cables with an ohm meter. If all switches are off and you have no resistance, you messed up and you will want to find the cause before you hook up and melt your nice new harness!
Let us know how it came out.
Kent