I think that is Haworthia attenuata. If you are growing it indoors right now and your indoor temps are high like consistently in the 80's, water it thoroughly once every two weeks. If your indoor temps are cooler like 65F, once a month. You have it in a glazed container, so you have to account for a longer drying time in the root zone. If soil feels damp do not water. I often put a small rock beside it, if I lift that rock and still looks damp, then I refrain from watering, especially during winter season.
And make sure your container has drainage holes, easiest way to kill succulents is to plant them in containers without drainage holes.
You can remove those rotten lower leaves, and allow the plant to dry and scab over those wet areas. Haworthias are toughies, given time to dry and heal, it will come back. You may also want to add some more pumice or perlite to your soil, so it does not seem to be too compacted.
