Victoria, if you are in S. California, I'd be willing to bet your beautiful agave plant is suffering from the heavy rains you had recently followed by cold weather. IF that's the case, there's not much you can do but wait to see if it recovers. Agaves can take heat and dry a lot better than cold and wet.
Still, you do need to cut off all the dead leaves, and clean up around the base of the plant for it to dry out and begin recovery. Please post more pictures, close up, and full plant after you've cleared the dead stuff, so we can see if the red spots are on the healthy foliage as well. That could indicate a fungal infection that you could treat.
Also pot up that little pup, as a back up! Good drainage is essential for those plants, so use a coarse cactus mix for it.
