Personally I don't think that "Wiring is Simple" or that snaking a new 12 volt line from the battery to a new accessory outlet, is a task for the electrical
systems impared owner.
1. It's not a cigarette lighter socket that's needed, it's a 12 Volt Accessory Socket... they are different. The Cigarette lighter socket is designed for intermittent use, the 12 volt accessory socket is supposed to be designed for longer term use and to physically support plug in devices such as small inverters.
2. There is no guarantee that the wire colors on the, always made in china, accessory socket will be correct. You have to know how to verify which one is which. Often they are not even attached.
3. Accessory sockets usually come with short Pig-Tails, to which the longer wires have to be spliced. Doing this correctly is a whole post on it's own.
4. The fuse holder has to be placed close to the battery in order to protect the unfused length of wire. Running a long length of wire before the fuse is an invitation for a fire.
5. Knowing how to safely secure and tie off the new wires also has to be done. Loose wires lead to broken or chaffed wires and/or loose connections.
6. And, unmentioned, is that an inverter will almost always still be needed to power the computers power supply brick.
As I said, I don't belong to the "Wiring is Simple" school of thought. I have repaired too many bad wiring jobs to ever suggest that.