[chandler48]

The first thing I would try is cleaning it with Murphy's Oil Soap. Then you can see what it needs.

 

[Half-fast eddie]

Looks like it might be water damaged finish.

 

[lenaitch]

The grain and wood patterns aren't matched so when you get it cleaned up you might find that the various shades are inherent. A gel stain might even it out, to an extent.

 

[carpdad]

Try these videos. I think the woman is more realistic. If you want the color to look original, only way is to strip, sand and refinish. Surface also looks like mosaic kind of different pieces of veneer and each piece will take stains differently which will require either pre sealing or some way to even out the stains at the end. According to her, those black specks are imitation so if strip, you will lose them.
Furniture strippers are toxic. Fumes too. Should do this outside or really well ventilated.

If finish is shellac, and there is no different finish or wax over it, you can dissolve the old finish with new coat and try mix it up. Better and certain is strip and refinish.

If not to that extent, try color matching. Paint store, not homedepot, show the piece and ask for best match. Then apply, feather to worn edge and wipe off after 10 seconds or so. If too light, try reapplying. It's important not to go over the worn edge. As mentioned, clean first.

Lighting makes a difference. If your light bulb is yellowish or white.