then i'd brush all the dirt and grime away with a soft bristle brush. hard bristle might leave scratch mark.
then use saddle soap for deeper clean. i'd avoid using normal soap as it'll dry out the leather.
rinse it, then i'd wet vacuum the thing to help remove any water. speeds up drying process.

then i'd dry it out in a shaded area, avoid direct sunlight.
maybe wire a fan to blow it so it'll dry faster.
or put dessicant silica gel to absorb any leftover moisture.

once dry i'd put leather conditioner to replenish the lost oil when we wash it.
leather balm is also good. or shoe cream which i think might do the same. or boot oil. or mink oil.

i don't have leather gloves i think it's too hot.
but that's how i wash and dry my leather boots. kena mud a lot.