How do you wash dishes by hand? There are dishcloths and sponges. People prefer one or the other.
I like dishcloths. They add color to the kitchen. They get into tight corners and narrow spaces. They go in to the wash. I use four or five a week depending on how greasy the dishes are.
A good friend buys dishcloths in bright colors and stacks them in an old crate on her counter. They are a cheerful spot. Another friend uses hand towels that are a size I would call finger towels. She always has two or three in use and puts them in the hamper every day or two.
I somehow got in the habit of making dish cloths. These dishcloths were made from a pattern featured on the Carol Duval Show on HGTV. I use Sugar ‘n' Spice cotton yarn when I have it. The smaller green dishcloth was knit using a "yarn" manufactured from corn stalks. It was an experiment. I don't recommend it.
You can also crochet dishcloths. 
If you prefer a sponge, good for you. Just keep it clean. These recommendations from WebMD suggest microwaving non-metal sponges and scrubbers for 2 minutes on a regular basis to kill germs and bacteria.
Or try this method from the Good Housekeeping Research Institute that says microwaves are unreliable and you should soak your sponge in bleach.
In any event, please throw out the sponge after a month.