How do you tell if a budgies ill?

Birds are very subtle in sickness body language, so you'll have to be very diligent about watching over your pet for signs of illness. Some signs may include refusal to eat, refusal to drink, drinking over the norm for your bird, not pooping, poop is suddenly a weird color and you haven't made any food changes lately, stuff is coming out of the nose, crusty stuff around the eyes are dull, feathers are dull, and many other things. If your bird is behaving oddly, keep a close eye on him/her for a day or two. If nothing changes, take him/her to the vet.
If your bird has really obvious signs of illness, such as sitting on the bottom of the cage, complete refusal to eat(not even his/her favorite treats), complete refusal to drink, or something else that you can obviously tell something funny is going on, take your bird to the vet IMMEDIATELY. Birds are only very obvious they're sick when the sickness has progressed in the bird significantly. Birds act like this because they're prey animals and predators usually go for the young, the old, or the sick, and so your bird wants to eliminate as many signs of sickness as possible, so it's a big fat red flag when your bird is obvious with sickness signs.