Here you go. These are my detailed notes.
There are generally two ways to brown a barrel. The hot brown method and the cold brown method. Most prefer the cold brown though it takes longer. Each method can be performed a couple ways. Color is controlled by the amount of carding, the method of carding, temp and humidity, and number of applications.
Barrel preparation is the same no matter which way you intend to brown. Browning does not work well on highly polished surfaces. Draw filing to remove the milling marks and square up the corners is a must and is all that is really required. This will give a more textured finish. For a smoother brown polish to 320 grit with the paper backed with a hard object to maintain the sharp corners. A finer polish results in a longer browning process and may result in areas not taking the browning. Polish no finer than 320 for browning. Now you need to degrease the barrel. Once degreased, handle only with gloves. I use rubber exam gloves but any rubber glove will work. The key is not to transfer oils from your skin back onto the degreased barrel that will result in a spotty finish.
12 hour cycle Cold Browning: I have had good success using Danglers Brown, Wakegan Bay Brown, and Laruel Mountain Forge Browning solutions. The first two must be put on so the barrel is just damp. Any heavier and you will impart a copper color to the barrel due to the copper in the solution. The only fix is to remove the finish and start over. With the barrel prepped and all holes plugged with wooden dowels apply a light coat of solution to the barrel using a clean cotton cloth. You need only dampen the metal. Now set aside for 12 hours to rust. Depending on the temperature and relative humidity this first cycle may only result in a dull greenish color. If so, do not card the metal. Simply apply a second light coat of solution and set aside for another 12 hours. Once a light coating of orangish rust appears rub/buff/card it off using 0000 steel wool that has been run through the dishwasher or washed in acetone to remove the oils. Wipe with a cotton cloth and repeat the cycles for three to five days until desired texture and color is achieved. The heavier you card the smoother the texture. A darker color can be achieved earlier by carding with a piece of denim during the first rusting cycles until the rusting gets more aggressive when you will want to switch to steel wool. The 12 hour cycle is convenient because you can do this over the course of a week before and after work. The 12 hour cycle is more aggressive since the solution has had more time to work between carding cycles. If you know you will miss a carding cycle do not apply the solution prior. Enough solution will remain after the last carding to allow a slower less aggressive cycle for when you get back to it. Do not let it go more than 24 hours without carding and do not skip a carding cycle often as it will result in a very rough surface. It will not hurt anything to go as much as 14 or 15 hours between a carding cycle should something arise. Cold browning is very forgiving.
3 hour cycle Cold Browning: Everything is the same as the 12 hour cycle except you card every three hours. This can give you a nice brown in a day as opposed to 3 to five days. Desired color is often achieved after about 6 to 8 cycles. Again try not to skip carding cycles. Since the solution has less time to work between carding cycles the resultant surface texture will be much smoother.
Alternately you can use Dixels scratch wheel (order from Brownells)