You can most certainly apply a ceramic coating to your car's paint yourself, and in fact, it's not terribly difficult to do. There are a few things you'll need to make sure you have on hand before getting started though. You'll need a quality microfiber cloth or two, some rubbing alcohol, and of course the ceramic coating itself.
Once you have everything gathered, the first step is to wash and dry your car thoroughly. Once it's clean, use the rubbing alcohol and microfiber cloths to give the paint a good once-over, removing any contaminants that may be present. Once that's done, you're ready to apply the coating.
Simply follow the instructions on the product you're using - typically, you'll want to apply it in thin coats with a foam applicator pad or something similar. Make sure each coat has fully cured before applying the next one (again, consult your product's instructions for guidance here). And that's really all there is to it! Once you've applied the desired number of coats (usually 2-3), simply stand back and admire your handiwork.