This is going to be complicated
So the fate series has multiple releases
But the main canonical storyline has three releases
Fate/Zero (the source material is a light novel)
Fate/Stay Night (the source material is a visual novel)
Fate Hollow Ataraxia (the source material is a visual novel)

Now if you want to get into the fate series most people recommend that you play the fate/stay night visual novel first (which clocks in around 60 hours)
Then play hollow ataraxia (which is 50 hours)
Then get into fate zero

Now that this is clear... Let me get into the anime specifics

Fate is a lore heavy franchise so people suggest that one must read it's source material to get deeply involved in it than watch the anime

Anyways
Fate/stay night can be said to be where the current events take place;
Also fate/stay night is a VN with multiple routes which somehow connect in the end and come together
There are three routes

1. Fate route
2. Unlimited Blade Works route
3. Heavens Feel route

Currently we have anime adaptations for unlimited blade works and heavens feel by ufotable.. studio seen made an anime for the fate route.. but it sucks so people don't recommend it..

Fate zero which is a prequel to fate/stay night has also got an anime adaptation praised for being excellent made by ufotable as well..

Hollow ataraxia doesn't have any adaptation as of now

So what's the watch order
If you only watch the anime
You can start with

1. Unlimited Blade Works anime by ufotable
2. Then watch Heavens Feel Movies by Ufotable
3. Then watch fate/ zero by ufotable
   (This is highly debatable and some people say you can watch fate zero first.. but it's a prequel so I won't be doing it)
   But the fate fandom warned me that watching the anime In any order will spoil something important.. also since the fate route from fate/stay night isn't animated in a good enough manner, thus experiencing the series via anime will be result in an incomplete experience
   so you know all this is messed

That's why
Most fate fans agree that
You read the
1) Fate stay night visual novel (which has all three routes)
2) Then read hollow ataraxia
3). Then watch the anime of UBW and heavens feel made by ufotable
4) And then watch fate/zero anime made by ufotable

Does this make it clear
Or do you feel an urge to kill yourself ?
??
Understanding the watch order is a pain in the arse
Lol