I looove vintage teak veneer sideboards, and I was inspired by skinnycat's post in this forum:
http://www.jumbletown.ie/forums/showthread.php?t=78820
Not long ago I got my hands on one that needed som serious TLC. As the before pic shows, the top had watermarks, heat rings, scratches and stains from both nailpoilsh and red candlewax. The front was mostly sticky and grubby with dirt.
So I looked at how skinnycat had done, and googled for even more info.
Top tips: Sand along the grain of the wood for a smooth finish.
I sanded the top, first with my mouse sander, then fine 240 grade sandpaper, then black 600 grade sandpaper. Lastly I used 00000 grade steel wool. Then I cleaned the top with methylated spirits, let it dry, and sanded lightly again with the steel wool. I vacuumed and wiped off the dust with a slightly damp rag, then let it dry again. The second before pic is how the top looked after the sanding.
Then I oiled it with teak oil, waited about half an hour, wiped off any excess, let it dry over night, oiled it again. I did this about 4 times.
The sides and front of the sideboard were actually not bad after I had cleaned them, just dry and dulled and the varnish was worn away in places. I just wiped them with teak oil and wiped it off straight away with a clean cloth, and that brought the lustre back.