Combs and boar's hair brushes are important tools for any man with a slightly larger beard, with brushes being a little more versatile as they work well for those that have shorter beards too. Keeping these tools clean and sanitary should be a priority in your beard maintenance, but they don't need to be cleaned often (barring you're not a barber, in which case they need to be cleaned in between every customer they're used on).
Your combs for personal use really only need to be cleaned every month or two, with acetate combs like Kent needing cleaning less than often than wood combs, since you can rinse your plastic combs through water after every use, whereas you don't want to be constantly getting your wooden combs wet — if you do, it's fine and you just need to wipe them dry. Boar's bristle brushes need cleaning only about 3-5 times per year, depending on your usage of it with oils and how much your facial skin flakes on you.
How to Clean Your Beard Combs
Grab a semi-large bowl or small tub; something large enough that you can place your combs into. If you've just cleaned and sanitized your sink, you can fill that up instead.
For a lot of combs, this should be sufficient enough to get them nice and clean. Consider using a small scrub brush and agitate the combs with it to get them extra clean. This is particularly important if you use oils in your beard, so you can remove any build up and residue on your combs. If you don't have a cleaning brush, use a cloth and soak it in your shampoo-water solution. A brush will be more efficient at getting in between the comb's teeth, however.
How to Clean Your Beard Brush
Use the same water you just placed your combs into to save time.
If you own a pair of electric clippers, you'll likely have had a thin cleaning brush that came with it. Those are perfect for reaching through the boar hair and getting to the wood.
After cleaning the brush, use a dry cloth to dry it as much as possible and set it bristle-side down to complete the drying. Optionally, completely dry it using a blow dryer.
Regular upkeep of your valuables will keep them doing what they need to: caring for your beard hair and the skin underneath it, without spreading unwanted particulates. A clean comb and brush is a clean beard!