There are multiple non-destructive methods to detect delamination in composite materials.
In case the delamination occurs on the surface, it can be easily found by visual inspection. This is the easiest method to detect delaminations; however, this is useful only if the delaminations are visible from the outside (i.e. they are on the surface), which is rarely the case, at-least in aircraft.
Ultrasonic testing- In this method, ultrasonic waves are passed through the surface of the material and the response is monitored. Depending on the condition of the material (whether it has defect or not), the ultrasonic waves behave differently.

Source: cnde.iastate.edu
The ultrasonic method used can be through scan (with the transmitter and reciever on the opposite sides of the part) or pulse echo method, where the transmitter/reciever 'listens' to the ultrasonic sound reflected back from the defect or the other end of the part. There are three main methods of ultrasonic scanning in use:
The A-scan presentation displays the amount of received ultrasonic energy as a function of time.
The B-scan presentations is a profile (cross-sectional) view of the part. Here, the travel time of the sound energy is displayed along the vertical axis and the linear position of the transducer is displayed along the horizontal axis.
The C-scan presentation provides a plan-type view of the location and size of defects.
Tap test, using a coin or an instrumented hammer- This is the most widely used method in the field as it requires minimal instrumentation. However, it requires a trained operator, who can distinguish between the normal and delaminated composite from the sound. Instrumented hammers are also available, where the frequency response of the part can be analyzed for identifying defects.

Source: amumagazine.com
- Thermography- Here, an energy source is used to produce thermographic contrast between tthe defect on the part. This is useful in detecting shallow subsurface defects, but is rarely used in field operations.

Infrared thermography Source: seattleinfrared.com
- X-Ray radiography (or CT scan in some cases)- This is a very accurate method for detecting internal defects; however, the equipment requirements mean that it is usually used in the place of the OEM, though some field equipment is available for military uses.

Fatigue crack under X-Ray, Source: vidisco.com
There are some other methods like the acoustic emission and lasers, which also can be used for detecting delamination. The table below gives some of the methods used for detecting defects in a manufacturing environment

Source: amumagazine.com