The cabinet you show was not painted it was stained.
It has water damage, some splits in the wood, ( maybe more where we cannot see).
There is evidence of mildew growing in the grain, the clear finish is pealing.
This piece can be renewed, but it will take great efforts and a fair amount of time to make it look new.
If you want it to simply be better aesthetically, you have a few choices.
All the options start with a cleaning and sanding.
Remove the knobs and hardware.
Get a plastic putty knife and scrape off the pealing finish.
Sand the cabinet box and the doors. (I like to start with 150, then 220 and 400 to a final sand with 600 grit paper.) Get all the previous sealer off, making the surfaces smooth.
You can treat the dark areas with 50/50 bleach and water to kill the mildew. Sand again with 600 grit after the treated areas dry. Apply stainable filler to any areas with splits or cracks and sand when dry.
Now you have options. :
1- If you want to re-stain, continue to sand all the stain off, getting in the nooks and crannies down to bare wood. Apply stain. Seal with at least 3 coats of polyurethane, lightly sanding between coats.
2- You can give an "old distressed" look by leaving some old stain and staining over it. This will give an uneven appearance that sometimes is good for blending the decor, but some people do not like it. Seal with three coats of poly again.
3- You can prime with a primer /sealer and then paint the cabinet any color you choose. There are specific paints for cabinets, but I have had good results with a number of quality latex paints. ( An inexpensive sprayer helps make this job easier and quicker.)
You can replace the cabinet with something new.