That all depends on what kind of a drink it is.
If it's a beer or wine, the first thing would be to get an EIN (Employer Identification Number) from the IRS and open a business bank account. Then you would need to go through the ATF's TTB (tax department) and get federal wine/beer permits, then the same permits in your state (if you state requires them). You would also need to file for excise taxes, register with the FDA, and trademark your company and products names. The process is a lot longer than this sounds, and there is a ton of paperwork to file.
If this is a distilled product, then it's almost the same process as beer & wine except it's a distiller's license ($1000 a year).
If this is just a mixed drink recipe, then all you can really do is submit it to the assorted bartending and recipes websites and books. There is really no way to market a mixed drink or cocktail like there is with beer & wine.
If you are serious about this, and it's beer, wine, or a distilled spirit, feel free to email me and I will help you.