"Cycled water" doesn't help, but adding sand/gravel, rocks, driftwood, filter media, etc, etc from mature tanks will surely transfer some "good bacteria" into your new tank.
There are a few approaches to 'cycling' a tank. Do some reading and decide if you are cycling with or without fish... Then decide which method of doing so you are going to follow.
Also, as mentioned, there are additives you can use to "instant cycle" a tank. When they first came out most experienced hobbyists were very skeptical and the first couple versions came with mixed reviews. By now the scientists have worked out most of the kinks and they have eared a respectable reputation. Just do some reading to be sure you buy the quality brands and not the knock offs which ride the reputations of others.
There is no simple answer to your question of 'how long will it take' as the answer will vary over a very wide range depending on many details. So be sure to choose a specific approach and learn how to properly adhere to that specific approach. As important details will differ from one approach to another.