EvilDragon16 said:
Well first you'll need to understand the situation .
The Fate franchise is based on a Visual Novel (VN) which was released in 2004 .This VN had three routes (paths the story can take) ,namely ;Fate ,Unlimited Blade Works and Heaven's Feel .The VN was successful enough to warrant the writing of a light novel going by the name of Fate Zero .A story of the events that transpired in the 4th Holy Grail War (The one in the VN is the 5th) .Though it is a story of events before those in the VN it was released with the intention for those who had already read to VN to read it .In short while it is a prequel to Fate/Stay Night as a whole ,FSN isn't a sequel to it .As for order since you're a newcomer I will recommed this if you want to watch the entire series .
Fate Stay Night (By DEEN) >Unlimited Blade Works >Fate Zero
But this is also a slightly tricky situation .The DEEN adaptation of Fate is regarded as a botched one .It doesn't properly adapt the first route and takes in events form other routes as well .Because of this it's a confusing adaptation for someone who wants to enter the franchise as a whole .So I don't think it's necessary to watch this one .Assuming you take that advice and watch only UBW (the series not the movie .The movie can't possibly give you a good experience) and Fate Zero then watching Fate Zero first isn't a problem .
Another thing is that the UBW route is in truth not a good adaptation as far as characters are concerned .It didn't properly showcase the sides of its cast .The main problem in the adaptation itself is the protagonist .To many on this site he seems like a bland person but that's due to UfoTable's adaptation effort .If you find him insufferable then I recommend rewatching the series and then looking at why he does what he does and not what it is that he does .
The movie is even worse .For the details on the Nasuverse (Fate's world) worldbuilding and explanation of the powers used in it you can go to this site :
http://typemoon.wikia.com/wiki/TYPE-MOON_Wiki
Some questions might be asked at how certain things happened so the link should come in handy .Ultimately I'd say you should read the VN but I doubt you'd want to sit through 50 hours of material .