In the old days, we used to use holy stones or griddle blocks on the teak decks of the old schooners because these would sand down the teak evenly, not pulling out the softer wood as above. Then we used a mixture of boiled linseed oil and kerosene to saturate the teak. It was a job for the whole crew, excepting master and cook, going up the decks en masse on hands and knees.
Today there are a variety of cleaners/bleaches (I like Snappy Teak the best) that do a marvelous job of cleaning and brightening teak, being sure to always go across the grain when scrubbing. There are also a number of finishes if you want to go that way, though most leave them to go grey.
However, and this is a huge factor, if you live or are going anywhere warm, teak decks get way too hot to walk on barefoot, let alone lay out on. For good maintenance in the tropics with the normal, relatively thin teak decks on yachts these days, they need to be washed down with seawater several times a day, which of course, turns them grey faster. They absorb a lot of heat from the sun and keep the cabin warm much later in the evening than glass, which is a pain in the tropics.
My first big boat, a Lester Stone Phill Rhodes racing cutter had real teak decks (no backing, so no rotting plywood underneath). Within the first year, I had to re-caulk every seam. It was back-breaking work, but done right it can last many years.
Almost every serious cruiser I've known who have had trouble with their teak decks has just removed them or covered them. If you are buying a showboat, then the teak is way worthwhile. If not.....