This one has been debated back and forth. My opinion remains that endoscopy is the best way to do it.
The two main ways are direct endoscopy or lateral neck X-rays. Lateral neck films are quick and comfortable; however, they involve a dose of radiation and are static images of what really is a three-dimensional space. Even more importantly, the image is altered and unreliable if the child is mouth-breathing, crying, or swallowing. These actions can falsely make the adenoids appear large. Furthermore, many radiologists aren’t so good and consistent about assessing adenoid size.
Flexible endoscopy does not involve radiation and is well tolerated by > 90% of all children. Importantly, you get an immediate answer from your doctor about adenoid size rather than having to come back for a follow-up appointment. Most importantly, findings on endoscopy correlate with obstructive symptoms better than X-rays do. Also, there is no real cost difference between the 2 modalities.
This is why I recommend endoscopy up front for kids. You get a more accurate, immediate answer, without incurring unnecessary costs or radiation exposure!