Do you wet the sponge when soldering?

Yes, if you're using the traditional cellulose sponge that comes with most irons and stations — it needs to be damp, not soaking wet, to clean the tip properly. A bone-dry sponge won't lift old solder and oxide off the tip, and a dripping-wet one causes a small thermal shock every time you wipe the tip, which over time can shorten the tip's life and cause the temperature to dip right when you need it steady.

The alternative many stations now ship with, or that you can buy separately, is a brass wool (coiled brass shavings) cleaner instead of a sponge. Brass wool is used dry — you just wipe the tip through it — and it's gentler on the tip over the long run because there's no thermal shock, though it doesn't scrub off heavy carbon buildup quite as aggressively as a wet sponge can.

Either method is fine; the point is cleaning the tip between joints so old, oxidised solder doesn't build up and block heat transfer. See how often should I replace a soldering iron tip for the wider tip-care picture.