Brushing is using a paint brush to apply glaze to a piece of pottery. In many ways it is a simple way for beginners; it doesn't require much in the way of equipment, you don't need to have a lot of extra glaze, and you can control where the glaze goes; but it is time consuming. Even if you don't want to paint or brush glaze on to your pieces I recommend keeping some brushes around for touch up, detail work and those times when a specific glaze really does need to have the top coat brushed in order to get its full effect.
The brushes that I like best for pottery are the ones found in my local craft store near the acrylic paints and other similar brushes. They generally have plastic handles and come in a variety of brush shapes and sizes. If this will be your primary glazing method I recommend getting a variety of sizes in flat and round brushes and getting duplicates.
Flat brushes are great for covering lots of area. Getting some flat brushes that are the largest size you can fit in your glaze containers can seriously decrease the amount of time that you spend glazing your pieces, especially if you are making items like large bowls, plates, and platters. I have found that a two inch brush fits in the short style 16 ounce containers and is useful enough to justify decanting glaze from a tall style container (such as those used by Amaco for their Potters Choice glazes) into something with a wider mouth. As wonderful as the big brushes are however, you will also want some smaller sized ones to handle other tasks, including pieces where a 2 inch brush is just two big. To start out, I recommend getting a pack of brushes with a variety of sizes so you can experiment and see which sizes work best for your personal style.
Round brushes are for detail, especially if your pieces have crevices that they you need to get glaze into. Round brushes can also be good if you are adding a design over your bottom coat(s) of glaze or if your piece has texture or design pressed into the clay that you want to highlight by adding a different color.
The reason to have duplicates is because some glazes stain and others are highly susceptible to contamination. You do not want to use the same brushes for these. In my experience, glazes that are dark orange, dark reddish or black in their liquid state, especially if those will not be their fired colors, are the glazes that are most likely to stain. By stain I mean once the faintest hint of that glaze gets on a piece of bisque ware it is never coming off. These glazes also seem to be more prone to spreading than others as well and are difficult to clean off of brushes. Identifying which of your colors fall into this category and assigning them their own brushes can help you avoid accidental contamination.
On the other end of things very light glazes such as whites and transparent glazes are susceptible to being contaminated by pretty much anything else. Assigning them their own brushes can prevent you from discovering that your favorite clean white now has a decidedly pink tinge when fired - from a glaze that is not generally prone to staining. Do something to make which brushes go with which glazes easily identifiable to avoid mishaps. If you are using multiple colors in one day I also recommend starting with the lighter colors and gradually getting darker before ending with the stainers. This will reduce the likelihood of contamination through shared water and can reduce the amount of clean up you will have to do while brushing.
When applying glaze via brushing, try to keep track of the number of coats you use and figure out over time if you tend to paint the glaze on heavily or thinly. This can help you determine how many coats each piece needs in order to get the desired color or effects. Commercial glazes will often have a recommended number of coats, but I think it is best to use that as a guidelines combined with your own knowledge of your personal glazing habits. I have also found that I like to do something to remind myself where the coats start and stop, particularly when adding a second or third coat to a round item where the glaze may dry before I get back to my starting point. Sometimes this can be mitigated by picking a point and working at it from both sides, other times I consciously choose a feature, however small to use as a landmark. The frequent quick drying isn't all bad however as it is best to let the glaze dry between coats.
I like to paint my pieces starting with the outside so I can turn the piece over and support it from the inside without worrying that I will disturb the glaze. After the outside is complete, the piece can rest on the table while I glaze the inside.
Brushing is an effective way to add glaze to a bisque fired piece of pottery and every potter should have some brushes on hand in case they are needed, but it does take more time than other methods. I definitely recommend getting a big brush.