Standard industry practice is to:
-Start with everything clean and dry.
-put the antenna connector on and tighten it down a reasonable amount. Snug, but don't crank on it too hard.
-Run a layer of electrical tape over the connection so it's covered from the base of the antenna to past the end of the connector on the coax side. Some choose to put the tape "sticky side out" to make for a cleaner removal. Your choice.
-Make 100% sure to not block any weep holes on the bottom of the antenna. These are necessary for allowing condensation to drip out.
-Follow up with a coax sealing tape. This is a soft rubbery tape that you layer over the connection and mold around it. Extend from the antenna down past where the first layer of tape stops. Work it well to seal the seams, around the base of the antenna (don't block the weep holes) and around the coax cable.
-Follow up with another layer of electrical tape. Apply "half lapped and back", in other words, each pass of tape should overlap half the previous pass. When you get to the end, turn around and apply another layer the same way. Do not stretch the tape, just make sure it's tight. Also, cut it with scissors or a razor blade, do not pull the tape to break it. That will stretch the plastic but not the adhesive. If you do that the tape will unravel on it's own.
That's what you'll see done on a commercial site. You can purchase "waterproofing" kits that include what you need, but they can be a bit pricy. Nice thing about them is they come with a really wide roll of tape that makes for a nicer finished product that using the 3/4" wide tape.
I've seen installers use a product called "Skotch-Coat" over the top of everything. It's a 3M product that comes in a can with a brush. It'll put a final seal over everything. Unfortunately it's been outlawed here in California due to high V.O.C.'s. It's pretty strong stuff, so if you do use it, make sure you don't breath it in.
The drawback of the UHF connectors is that they are not waterproof and tend to have some pretty big voids in them when assembled. This gives a place for condensation to gather. Some use a foam injected material, but that stuff can make a real mess. Proper waterproofing should prevent issues.
Ideally, get the antenna with Type N connectors, if you can. They are designed to be waterproof and are a much better connector. Even though the have the waterproof design, you'd still need the steps above to seal it.