In movies like Teenage Mutant Ninja Turtles: Out of the Shadows (2016), how do actors make eye contact with CGI characters?
If you talk to actors that do a lot of CGI, the answer is "not very easily". (Ian McKellan famously almost quit filming The Hobbit because most of his work was acting solo, since they had to CGI in the hobbits later to make them short.)
However, there's a couple of techniques that pop up frequently in CGI-heavy movies:
The "tennis ball". Often an actual tennis ball, but not always. Some small prop will be held at what would be eye-level for a CGI character, and the actors play to that. Because the CGI is added in later, the FX team will just adjust their graphics so that the character shows up where the actor is actually looking, as much as they can. This technique is also used when actors need to maniuplate (touch, hold, pet, etc) CGI creatures, to give them something tangible to work with.
Stand-ins. For CGI characters that are mostly human-sized and human-shaped, often times the actor doing the motion-capture will just act through the scenes (dressed in a motion-capture suit) and be digitally replaced later on with their character. This was done in your example, Teenage Mutant Ninja Turtles, with live actors playing the turtles (click this still image for the video):
Sometimes they will combine the two techniques. In Age of Ultron for example, James Spader in motion capture gear plays Ultron throughout the movie, but early on the character becomes much bigger than a human. For those scenes, they positioned a set of red lights over Spader's head so the actors (in this scene, it's Elizabeth Olsen and Aaron Taylor-Johnson) would remember to look well above Spader's head when talking to Ultron (again, click for video):
For Avengers: Age of Ultron, they used a thing with three red dots on a stick to mark the eyes for the CGI Ultron character, actually played by James Spader. Actors would then have to look at these red dots while talking to Ultron.
Well, how would you know if they were actually making eye-contact? They look at a spot in space, maybe there's a marked portion of a wall that they are supposed to look at, and then, with CGI, you can impose the image wherever you want, so regardless of where the actor is looking, you can move the image there.
Keep in mind, even without CGI, how do they make eye contact? What we perceive as eye-contact, as movie viewers, is the actor looking directly into the camera, not into the other actors' eyes. Other than that, we can only see that they are generally looking in the direction of the other actor, unless they are nose-to-nose.