-Hydrogen Peroxide, in a spray bottle
-Unscented Antibacterial Foaming Soap
If by some chance your aquarium net happens to be covered in filth (for whatever reason) than you may want to try washing the net first with an unscented antibacterial foaming soap before attempting the below method, otherwise skip this step.
Start by liberally spraying your entire aquarium net (handle and all) with hydrogen peroxide. Let the peroxide work its cleansing magic for around 15-30 minutes (you may see the peroxide turn white on the net as it kills off any bacteria). Rinse off the entire aquarium net by carefully pouring on the boiling water. Shake off excess water from the aquarium net. Allow the net to air-dry overnight.
If your net is looking dry or you have numerous aquariums you're dealing with then you'll want to use a Net Soak solution as to avoid cross contamination between tanks and/or to keep your net conditioned so that the netting doesn't scratch/harm the fish. Net Soak will also clean your net, the one I use does not require rinsing and claims to not harm fish.