I wouldn't wring the brush out, wringing out might damage the bristles. What I do is hold the handle and flick my wrist aiming towards the sink. I do this strongly about ten times. Shaking it out more or less. I hang my brush overnight and use a rotation so they have a chance to dry out. Not everyone hangs them or uses a brush rotation but I'm just mentioning it since it is what I do.

Like Lynn says, keeping the scales dry during the shave is a good idea. After the shave I rinse the blade under the tap and dry the razor with a Kleenex tissue. I check the scales for any droplets inside and run the tissue through if there are any. I strop 20 laps on leather to get rid of any possible micro grunge on the bevel, wipe with a silicone gun cloth and put it in a dry place. Leaving water drops on a razor because I forgot to do this has resulted in water spots on the blade so I am careful to tend to it.