Begin by removing all trim that touches the vinyl roof and masking off both the car's windows and painted sheetmetal unless you like cleaning glue off of your new paint job. The masking needs to come right up to the outside edge of the chrome and detail trim lines. The roof has been primer prepped, and the new vinyl is sun-treated. Use a tape measure and a Sharpie to place two marks, one at the front and one at the rear, on the exact center of the roof for proper alignment. This is a critical measurement; double-check it before going any further.
While wild graphics might be the strongest visual memory of the supercar era, many of the performance cars built at that time were fairly upscale. Often, they received big options in addition to big engines. One of the nicest upgrades on the option list that required only a small premium was a vinyl top. In some special cases like the Superbird, the top was even mandatory in order to cover unfinished bodywork.
However, those sheets of vinyl that covered your musclecar from its creation until now have been subjected to at least 25 years of wear, and the effects of sunlight, weather, and general use often leave them in need of repair. Moreover, improper installation or damage often results in rust forming beneath the surface, leaving bubbles and body damage. Obviously, any serious restoration requires its replacement.
In more cases, the top had been stripped away when bodywork began. If not, plan on spending some time removing the trim, scraping the old roof and the residual glue, and prepping the roof like you would any other surface to be painted, stopping at the sanded primer stage. Before installing the top, mask off anything you don't want to get the contact adhesive or glue on. Pay special attention to window edges, the A-pillars, and the trim mounting points. The masking needs to leave the roof trim mounts exposed so the glue covers areas that will also be held down with screws or clips for the tightest possible fit.
If you're doing this yourself, purchase the correct top for your installation; this one came from the Paddock. According to Mike Paremsky, whose shop did the installation, the virgin top should be left outside, flat, in bright sunlight for a few hours to remove any wrinkles and minimize the risk of problems during or after the installation. Directions that come with the top should give specific information. The primary thing, like other quality automotive-finishing techniques, is patience.
The 1968-1970 Chargers offer some unique problems due to the flying-buttress rear-window design; the top will have to stretch over and down both sides of the C-pillars. As a result, doing the Paddock's Charger is a little more detailed than, say, a GTX from the same year. However, a majority of the points shown here will be applicable regardless of your body design.
We'll need several tools. While it's possible to apply the glue with a brush, a sprayer makes life easier and eliminates most chances for lumps or dry spots. A good vinyl-top adhesive is next, and buying a little extra is always better than running out before the job is done. At least one extra set of hands makes things go a lot quicker and easier as well. Finally, a pair of good scissors, rolls of masking tape and 1/16-1/8-inch-wide pinstriping tape, a razor blade or utility knife, a tape measure, a Sharpie™ pen, paint thinner for mistakes, and tools to attach trim and hardware should be at your disposal.
Now watch the experts at Michael's Auto Body in Winter Haven, Florida, reskin the Dodge.
Here's the mark on the car. | 
Fold the vinyl roof cover exactly in half. This needs to match your mark on the car, so be sure it is correct on both ends. Once assured, cut a small triangular notch on each end. Since this is extra material, the cuts will not hurt the finished install. | 
Test-fit the top using the Sharpie marks as guidelines. Make sure you were shipped the right example for your model, and eyeball the general alignment. There is extra material here, so it might be a little larger than expected, but it should appear to cover every surface without a problem. Due to the Charger's "flying buttress" rear window, it will not be perfect in this area before stretching. |
Once you're ready, fold the top over on itself again, exposing one half of the roof. This is the point of no return; recheck your alignment and get the glue sprayer. | 
The guys at Michael's use DAP Weldwood Contact Adhesive to attach vinyl tops. Since this is spray grade, there's no need to dilute it. | 
Using a helper, roll back the top even more while maintaining the material's position so that more of the roof is exposed. Spray glue about a foot wide on the centerline of the roof only at this point, as well as the back of the material in that area. Don't spray the edges of the metal yet. |
Evenly roll the top back over the roof again. This is tacky stuff; if the alignment is off, pull it up carefully by the edges, being sure not to stretch it, and start over. Ideally, the top will line up to your marks and you can begin stretching and pulling it. | 
If it's right, smooth the top carefully down the centerline to eliminate any air bubbles or ridges. Pull it over the front and rear of the car first to ensure it's still lined up, and then work your way down each side. | 
Now you're ready to finish applying the glue to the roof. Do this one side at a time. Lay a piece of tarp on the top half of the material you're not going to glue yet. Next, roll the material for the side you'll work on next back on top of this. Spray all the roof surfaces on the half you're working on, including A-pillars, C-pillars, gutters, and edges, feathering the glue down on the metal-appearing paint. Good masking in step one is important... |