I also heartily recommend taking the bird to a vet but I will
tell you of an experience I once had. I had about thirty Finches
and noticed one day that one had something dangling from its
leg. I captured the bird and discovered its leg was broken at
the knee joint.
Since it was obvious this was no recent injury as the part that
was dangling was all dried and the rest of the leg looked
healthy, I gritted my teeth and clipped off the part that was
dangling. There was no blood, but just to be safe, I gave the
stub a good cleaning and some peroxide and a tiny bandage.
After about a week, the bird had removed the bandage and it was
difficult to see which one of the thirty was the one-legged bird.
It occurred to me that unlike a human, a leg on a bird isn't
that big a deal. An injured wing is serious but a one-legged
bird can survive quite happily.
He had no trouble landing and was an active member of the flock,
but again, I stress that I was just very lucky and recommend
attention of a vet no matter how you can arrange it. My finch
was already healed when I discovered the broken leg but who
knows what pain he might have suffered during the time I was
unaware of the injury?