Proper care is to pot them in containers with drainage holes - are there any in those mugs? Well draining mix - yours looks very dark; maybe it's wet - can't tell from photo. And they need lots of light. These are basic needs of succulents.

The one on the right might be a graptopetalum. Regardless of the identification, follow the suggestions in the comment above.

Agree that one on right looks like a Graptopetalum, perhaps G. superbum. One on left could be Pachyveria glauca.

Rina is right. PLEASE take them out of that incredibly rich, thick soil and put them into unglazed terra cotta pots with drainage holes and a mix with half perlite....or you won't have any succulents within 2 months. We have all been there and done that....and lost succulents in the process.

Thanks everyone! I will try to follow all of your suggestions to the best of my abilities!