Most slippers come with cleaning instructions. Read them and follow them. Each pair is different and will need to be cleaned and treated differently. For example, slippers from sheepskin recommend that you use liquid soaps that are specifically formulated as non-enzyme.
To get the most life out of your slippers use them inside only. If you wear your slippers outside they will wear faster and will not be as clean as slippers worn exclusively indoors.
One important thing to note about memory foam is that some memory foam will emit a chemical like odor. It is more of a problem in mattresses and helmets than slippers. But there is a rare chance that it may occur with your slippers. Don't worry. The smell will fade over time and it isn't harmful. You could probably even return the slippers and get another pair just like it, without the smell.