Mint can be grown successfully in pots, but because of its desire to spread by underground runners, you will need to turn it out of its pot either annually or biennially, cut the rootball in half (I usually use a bread knife), discard any obviously dead growth (usually in the centre), and repot into fresh potting soil. Bushy, fresh growth will then appear. If you don't do this, the central part of the plant dies back and all you get is the odd stem or two at the edge of the pot - yours looks like it could do with dividing and repotting now.
In regard to moisture, don't leave it sitting in water, but water frequently, when the surface of the soil feels just about dry to the touch, and water thoroughly, allowing excess to drain away. If the soil in the pot becomes totally dried out and hard, you can revive it - just stand the pot in a large tray or bowl or something, water well so the tray ends up full of water, then just leave it like that for a few hours. The soil in the pot will take that water up and the soil will be moist again. The other option if the soil dries out, especially if the plant in the pot is wilted, is to sink the whole pot into a large bucket and anchor it down with stones or something heavy, so that its submerged in water. Leave for a few hours, then remove and allow to drain down.