what is the best way to restore teak outdoor furniture?
Sorry to be the bearer of bad news, but there is no magic solution you can spray on and restore the original beauty. As an owner or an older Carver with lots of teak, the only solution is to sand it down.  We solved the every year restoral ritual by using Seatrol medium sealer by Sikens. (found in marine stores)  Couple of coats of this stuff and your teak will look good for years.