I would amend Donna's post to say "If you're flying back nonstop to the U.S. you should arrive at least 3 hours prior to your flight." However, if your flight is a Delta code share actually operated by someone else (like Air France, KLM, or Alitalia), two hours should be sufficient.
If you really are flying on Delta "metal" (meaning Delta actually operates the flight) directly to the US, you report to Terminal 5 to check in and clear security, then you are bused back to Terminal 3. If you are taking the Leonardo Express, you make your way to the outside front of Terminal 3, where a free shuttle bus takes you to Terminal 5; you cannot walk between T3 and T5. If you are taking a taxi, be sure to tell them to take you to T5, so you don't have to take a shuttle after your taxi. Note that T5 is also used by El Al, so there are armed security guards inside and out, which unnerves some people not prepared for this. And at least in May 2014 when I used it, you had to remove all your "electronics" from your carry-on and place them in a separate plastic bag they provided. Their definition of "electronics" included not just phones and iPads, but also charging cords, so everyone had to rummage through their bags to find the designated items (I certainly would have packed differently if I had known this).
On the other hand, if you are flying on one of the European carriers (even if it also has a Delta number), you report to Terminal 3 to check in. Someone else here reported that the security was also less intense there (no need to remove electronics except laptops, for instance). So, you do need to find out who is operating your flight to make your plans.
