Can someone inform me on how to achieve this type of patina on a furniture project I am working on
Looks like an "ebonized" piece. That can be as simple as applying a black pigment or dye stain, or you can get fancy with some woods and do an iron-and-tannic-acid reaction to darken them a bit less unnaturally.

The metal pieces can be bought with dark anodizing or other treatment, painted, or you could try just hitting them with a black marker.

(I'd refer you go the woodworking area, but since this piece appears to be metal and plywood there isn't a lot of woodworking in it. That'd be the best place to learn more about staining and dying wood, though.)