You have a 5 year window which begins the moment you take part in your first practice. You can only play a maximum of 4 seasons during the 5 year window.
If a player uses a redshirt for the 2014 season, he will have playing eligibility for 2015, 2016, 2017, and 2018, but he'll have used up his one and only redshirt season.
If a player contributes as a true frosh in 2014, he'll have playing eligibility for 2014, 2015, 2016, and 2017 ... but he'll have a redshirt year, just in case he misses a season due to a serious injury. If he were to get hurt during the first half of a season, and he were to play less than 30% of the games, he could petition the NCAA to reclassify his partial season as a redshirt season, and he'd have eligibility in 2018. But you have to have a redshirt available in order to do that.
It's a common misconception that there are two different types of redshirt seasons ... that you can take an "academic" redshirt as a true frosh, then get a "medical" redshirt later in case of injury. This is totally false. You get only ONE redshirt season, and that's it. If you use it, you lose it.
There have been cases where the NCAA has granted a player a 6th year in their window, but that only happens in cases where players have been forced to miss TWO or more seasons due to serious injuries. If a player takes a redshirt purely as a coaches decision, there's no basis to get a waiver approved.
See Aaron Weaver as an example. He redshirted at Hofstra in 2006, and played 2007, 2008, 2009. Transferred to SU for 2010, but was injured 2 games into the season, and that was it for him. Now if he had been forced to miss 2006 because of an injury he suffered in HS, he could have petitioned the NCAA to get eligibility for 2011.