The being resembles a very large frog. However they are legless, and have a long lizardly tail. They also have a pair of webbed wings held off the ground like a bird
What is the most plausible way for these beings to take to the air?
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Have them coil up their tail like a snake would and then have them perform the striking action with the uncoiling tail's muscles like a snake does but instead of it having a purpose for attack have it launch them into the air.
I don't know the size of the wings of your creature so whether or not it can fly is something I can't answer with confidence, but it should at least be able to glide and extend the length of the glide with flaps.
They jump off a height and use the free fall to get the needed speed to fly.
For landing they need to slow down until they basically stall and do a controlled crash, and prefer doing it on elevated places, from where they can take off again.
This implies that they need to fully feed while airborne, thus they feed on flying insects and other small things floating in the air, which don't require them to land to eat.