Usually clinically. Most diagnoses are made clinically with signs of swelling. Unfortunately, by that time, there is already fibrosis and changes are controllable but not reversible. Phys ther often use tape measurements which can be very variable (location, tightness of tape, dominant vs non-dom arm). Water displacement works well but cumbesome. Bioimpedance is simple and reproducible but insurance won't pay.
Inequality. Whenever there is a swelling if it is asymmetrical then the swelling probably is lymphedema. It could be acute due to injury or surgery, ailments. If it is lasting a longer time then it is diagnosed as lymphedema (chronic typically is considered more than 6 months).
Same for all. As dr. Canale said, it is usually diagnosed clinically. Usually seen in women, lymphedema is a painless swelling of one leg, but it can be both. The hallmark of lymphedema of the legs is that the feet and toes are also swollen. If you can't pinch the skin on the top of your 2nd or 3rd toes because of swelling, then it is probably lymphedema. This is not true if you have edema from other causes.