The best way to play diplomacy is face-to-face. I would always recommend a face-to-face game over any version with e-mail/phone/whatsapp or whatever kind of interface.
Unfortunately I also know that not everyone – including myself – always has sufficient friends close by to play diplomacy face-to-face.
I will list a few examples of apps/website where to play diplomacy. However, it will depend on your own preferences and time/place which you will prefer. I personally like a version that is accessible both via phone and pc, as sometimes a map on a phone does not provide sufficient overview of the complete situation.
This is quite a new interface, developed by a few programmers. It works fine, communication tool via phone is okay-ish, but works perfect on your pc. I am quite a fan of this relatively new diplomacy-engine, and would definitely recommend it. See more here
You will notice that I give quite a few examples maps of situations that could occur on the board. I use the sandbox (simulation) tool from Backstabbr to create these situations. For Backstabb developers: Thank you for letting me do this.
This is an Android based app, it works fine, communication with other players is possible, but not ideal. It is better to type messages via the web interface, but you can notice most players are only active on their phone. Not my favorite platform. Formerly called Droiddippy. See more here
Most of the diplomacy games I have played, are via this tool. The interface is good, and also works fine on your phone. I am not saying this is the platform you should choose, but I had lots of fun on it. See more here
A European website. Interface works fine. I have to admit I have not got sufficient experience to give you any advice. See more here
Playing via e-mail is a little bit old school nowadays, but back in 2005 it was pretty normal that games were run via e-mail only. I believe nowadays, even if you want to play with a selected group of friends, just select one of the above platforms and start having fun.