I have just finished sanding a built in dresser for a closet. I am getting ready to stain it and would love to get the cabinet to match the wood paneling in the walls. Its all made (the dresser) with white birch. The paneling is the 70's grooved oak with a really high gloss. I can figure out matching the stain, but I was more curious as to how I get that high gloss look?

Use high gloss polyurathane if you want it to really shine. Apply one coat then very lightly sand, second and third coats may be needed but do not sand after the final coat.