If I remember correctly, the lighter socket belongs just to the right of the ashtray, under that flip-up door, right? Is there a metal circular trim panel in the place where the lighter belongs?
Firstly, I've never seen a good aftermarket cigarette lighter. Go to the junkyard and get a real GM one out of another van. If there are no vans, get one out of a GM truck or large car. Get a couple in case one is bad. Cut off as much wire as you can too.
If you have any luck, your van might be pre-wired for the lighter. Look behind the panel for a plug that has one orange wire and one black. Plug it into the lighter and see if it works.
If the van isn't pre-wired, you'll have to do it yourself. First, do whatever is necessary to get the lighter socket physically mounted into the hole next to the ashtray.
Remember where I said to cut out as much wire from the car at the junkyard as you could? Here's where that comes in. The black wire is ground.........use a crimper to crimp a circular ring terminal onto it, and then use a screw to attach it to a metal part of the van.
The orange wire needs power, so run it over to the fuse box. Make sure you tie it up in a way that it can't fall down on your feet and cause an accident.
Obtain an inline fuse holder and a 15-amp fuse. (You can usually find these at the junkyard too). If you have no fuse holder, most wire-crimping kits contain female ends that can be pushed onto the terminals of the fuse, allowing you to make your own fuse holder.
In any event, look for an empty slot on the fuse box marked "BAT." You can crimp a male end onto a wire and push it into the BAT slot. You want a wire to come out of the BAT slot, go into one end of the fuse, and then the other end of the fuse goes to that orange wire going to the lighter.
(It's easy for the terminal to fall out of the BAT slot. Tie it up in such a way that it won't shake out by accident.)
The idea of the fuse is that if by accident, the orange wire gets shorted out, the fuse pops right away. Otherwise, the orange wire will melt, ruining your whole day.
When the lighter is connected to the BAT terminal, the lighter will work at all times, regardless of whether the key is on or off. If you instead hook it into the IGN slot, it will only operate when the ignition is on...........GM does it the first way from the factory....but it's your preference.