Generally speaking, electronics like that is working at very low voltage, so water damage happens slowly. Take the batteries out. Dismantle the casing as much as you can/dare. Place it somewhere pleasantly warm but not unpleasantly hot. The dash of a car is good, an airing cupboard is also good.
Leave it for a couple of days. DO ALL THIS AS SOON AS POSSIBLE!
After that, you can make sure of the job by putting the meter (still in pieces) in a lidded container with some silica gel capsules, but only if you have reactivated the latter by heating gently, eg in a slow oven, for an hour or so.
I used to run home-made stand-alone electronic devices in the field for my job (wildlife research), so I have plenty of experience of resurrecting waterlogged units!