How can I refinish a 4 drawer black filing cabinet to look better?

You can paint it! Prep it really well, here's a tutorial on painting furniture.

Cheryl...You can also use contact paper or mod podge with 1 ply napkins. Maybe doing the painting then one of the other on the drawers. Good luck..be sure to send us a before and after picture when you finish.

Use spray paint for best results.

The easiest to get good results is to use spray paint. Sand off any rust. Then clean off any dirt, first with water. Dry well and then with plenty of ventilation, preferably outdoors, clean off with paint thinner to remove any oils.

When 100% dry, mask all parts you don't want to get painted with masking tape. Fold some ends of the tape to make it easier to get a grip when removing the tape afterwards.

First spray on metal primer. Spray a bit on paper to make sure the spray can is working well, without drippy spots. If it is good, spray a light coat, moving constantly to avoid thick application areas. Primer helps the new colored paint adhere. It does not have to be durable. A thin coat does the job.

Let dry completely, which varies with the temperature and humidity. Sunshine helps paint dry and cure.

When totally dry, using the same technique, spray your first thin coat of finish paint. After it is totally dry, then spray another light coat, moving constantly and shaking the can often.

Rustoleum sells a product called 2X that says it does priming , too. I have used it for outdoor garden applications on rebar and trellises, but not on large flat surfaces. Perhaps the hammered paint, which probably needs a primer, would be good for hiding imperfections better. It comes in a couple of colors, gray for sure.

Here's a fun way: https://www.hometalk.com/diy/home-office/furniture/glamorous-file-cabinet-makeover-1961972

Glamorous File Cabinet Makeover