I've used two different processes, both successfully. Each has it's own 'tricks'.
1) Birchwood Casey Plum Brown. This is a hot process; you heat the metal and apply the browning solution with a large cotton swab. The key is to thoroughly clean and degrease the metal first. This makes handling the parts an issue; nitrile gloves are the solution. Two to four coats are usually necessary. The first one will appear uneven but that's quickly and easily fixed with the following coats. Also, if one of the coats is uneven, due to the metal cooling too fast, fixing it by applying another coat is easy and effective. Pros of this method are speed (you can apply several coats in one day) and control (each coat gives a darker and smoother finish and you can quickly judge whether to add another). Plus you don't need to plug the bore because the interior of the barrel doesn't get hot enough to react with the solution if any should get inside. Cons are the need to keep the metal clean and degreased, so plan how to handle the parts in advance.
2) Laurel Mountain Browning and Degreaser Solution. This is a cold process; you create a high humidity environment and apply the solution, then let it rust for several hours. The parts are then 'carded' with a stiff brush or denim cloth to remove the scale. Several coats are necessary and it will take a couple of days to complete one gun. Warning: the first coat or two will look terrible, but each subsequent coat will get better. Pros are the humid environment is easy to set up (I just turned on a hot shower and closed the bathroom door) and the solution is itself a degreaser, so keeping the parts clean and grease free is not as important. Cons are the time invested - it takes much longer than the hot process. Also, you will need to plug the muzzle and nipple/touch holes to keep from rusting the bore.
Both will give a deep, smooth brown finish, and both can be tailored to produce the amount of 'antique' that one desires.