Well, you can watch the movies in the following order:

First, X-men First Class, as it depicts how Professor X and Magneto met.

However, in order to watch X-Men Days of Future Past, you have to watch the original trilogy. You should finish X-Men, X2 and X-Men the Last Stand.

You can also watch X-Men Origins Wolverine Before original trilogy, but

there is a cameo appearance of Professor X. However, by watching this movie, you will know how Logan got metal claws and help watching X2.

So X-Men and then X-Men Origins Wolverine.

Once you have completed these movies, see The Wolverine, as

it has a scene that is related to X-Men Days of Future Past.

It also shows events took place in Wolverine's life after what happened in X-Men the Last Stand.

After that, watch the upcoming movie, X-Men Apocalypse.

CONCLUSION

The Order of the movie can be:

1. X-Men First Class
2. X-Men
3. X-Men Origins Wolverine
4. X2 X-Men United
5. X-Men The Last Stand
6. The Wolverine
7. X-Men Days of Future Past
8. X-Men Apocalypse

Deadpool is also a part of X-Men series, but it is not related to any of these movies. However, one can see it after X-Men, or as per comment by cde, X-Men Apocalypse.

Edit after release of Logan

Logan movie is set in 2029, after X-Men: Days of Future Past. So it can be watched after DoFP without requiring to watch Apocalypse or any other movies if you have character knowledge as mentioned on my other answer.

First thing first, X-men was never tightly paced up chronologically and it do have many canon issues.

But I do want to suggest to go by release order:

First watch X-men 1 to 3. X-men 3 was a disaster film but it is important for understanding The Wolverine.

Then go for X-Men Origins: Wolverine, which is a prequel and give you back-story of Wolverine, most of it is weak and unnecessary and it's not even canon anymore with X-3. Which I have discussed in my own answer here but it have Deadpool origin spoiler from X-men Origin and Deadpool film. (X-men 1 and 2 too are also not much of canon, but they are better treat to watch).

Then go for X-Men: First Class which is prequel to all the rest of films, you can watch it at first place but it's not going to help much and it also have many inconsistency with rest of the films which was fixed by it's sequel a bit.

Then The Wolverine came which can be watched anytime after X-men 3, no need to watch First class before it. But it's end credit scene is a setup to it's sequel , X-Men: Days of Future Past.

X-Men: Days of Future Past is sequel to X-Men: First Class and X-men 3 and it also set up a tight canon and made X-men Origin and X-men 3 non canon and X-men 1 an X-men 2 too to undefined extent for now. Not sure how much The Wolverine is canon now.

Then comes Deadpool, which works standalone but did made reference to X-Men Origins: Wolverine and X-Men: Days of Future Past. For detailed answer from scifi refer here.

So I suggest to go by release order, if want to make short-cut then avoid X-men 3 and just read it's synopsis before watching The Wolverine and watch X-Men Origins: Wolverine just to see how badly Deadpool was handled before it's redemption in Deadpool film.

1962 X-Men: First Class

    Cuban Missile Crisis , 1962

1973 X-Men: Days of Future Past

    1973 is clearly stated in film.  This is after Wolverine left
    Stryker's group, but before his "lumber-jack" job.  This film is  
    in the middle of "X-Men: Origins: Wolverine" and start with an alternate 
    timeline that ends up never existing because a new timeline is put in place.

1970-80 X-Men: Origins: Wolverine

    This covers Wolverine's past, but takes place 
    during Vietnam and through the 1970's up 
    until 3-Mile Island ( 1979 ).
    Wolverine's MIND is WIPED and he is ENCAGED as 
    "WEAPON X"

1984 X-Men: Apocalypse

    Wolerine (Weapon X) is RELEASED from his CAGE, about
    15-years before the 2000 X-Men film, and
    Jean restores a few of Wolerine's memories.  

2000 X-Men

2003 X2

2006 X-Men: The Last Stand

2013 The Wolverine

    This is after the "X-Men: The Last Stand" film.

2016 Deadpool

For the best overall narrative and least amount of inconsistency, I'd suggest the following order (note: I am omitting some of the films due to quality, consistency, and narrative issues).

1. First Class (obviously)

2. X-Men

3. X-2

4. X-Men United (optional because it isn't very good, but is pretty important to fully appreciating the ending to DofP)

5. Days of Future Past

6. Logan

I left out Origins and the Wolverine because they are more side stories that distract from the main X-Men narrative (that are already heavy on Wolvie) and Deadpool because it just similarly doesn't belong at all. I also leave out Apocalypse which is alternate/ branching timeline stuff (and a pretty lame film). That being said, I recommend everybody to check them out after watching the others if they are interested.

This the correct way and why SPOILERS FOR DARK PHOENIX

1. X-Men First Class
2. X-Men Origins Wolverine (never happened after DOFP)
3. X-Men (never happened after DOFP)
4. X2 X-Men United (never happened after DOFP)
5. X-Men The Last Stand (never happened after DOFP)
6. The Wolverine (never happened after DOFP)
7. X-Men Days of Future Past (only Wolverine remembers events in 3-7) whole new timeline created after first class, different events happen to get characters to where they are in the end of DOFP.
8. X-Men Apocalypse
9. Deadpool
10. Deadpool 2 (Ik Deadpool is before Dark Phoenix because in it they refer to the school as Xavier’s school. Where as in the end of Dark Phoenix they refer to it as Jean Greys school.)
11. Dark Phoenix (Jean is Alive at the end and that is how she makes it to the end of DOFP)
12. Logan (Wolverine lives a long life ((now remembering his prior timeline and this timeline)) and teams with the x men for many years after DOFP, until he is ultimately led to here)

The only way it makes sense is

1. X-Men First Class
2. X-Men Apocalypse
3. X-Men Origins Wolverine
4. X-Men
5. X-Men United
6. X-Men Last Stand
7. The Wolverine
8. X-Men Days of Future Past
9. Logan.

Deadpool now works because the past was changed in Days of Future Past and X-Factor Deadpool may have never been created.