Can someone explain to me how evolution will work to make the frogs survive?
No. We can speculate on what
might happen to the population, but since evolution is not pre-ordained or goal oriented there is no direction in which to say how it "will" solve this problem.
I like Asking's treatment in message 16.
However, camouflage (or extinction) may not be what happens. There are a whole host of other probabilities within biological systems. The same kind of scenario as skin color may involve skin taste or poison instead. So a bunch of bright green easy to see froggies survive in the open because predators learn to avoid them.
They may, for all evolution cares, mutate into froggie equivalents to pink elephants and fly away on Dumbo ears (though I wouldn't count this one as very highly probable).
The point being, no one can say what will happen. All we can say is that since the environment is dramatically changing, the species will change (in some unpredictable way) or die.