It looks really wet...it is probably rotting. Take it out of pot asap, shake off all the soil, put it on some newspaper & hopefully water will soak in. Then inspect the roots, see if they are firm or soft, mushy, slimy - hopefully not.
Soft leaves are probably goners, if so hopefully you can save the center rosette & it may grow.

how long should it stay out of the soil for?

Certainly looks like it's in trouble. Agree with Rina. The thing is, leaving it out to "dry" may not be the total answer. As Rina said, if there's rot, the only thing to do is cut the stem back to healthy tissue, allow to callous for several days and plant in some type of gritty mix and water VERY sparingly, if at all until new roots appear on the stem. If all else fails, not to worry as this is a somewhat common Echeveria and it wouldn't be the first plant most of us have lost! If you can't locate more at a BBS, let me know as I'm certain we can work something out.