If the top epidermal layer is burned away, what is it replaced with?
The epidermis is a four- or five-layered epithelium. The top layers are squamous whereas the bottom ones are more columnar (http://en.wikipedia.org/wiki/Epidermis_(skin)). The lowest layer is separated from the dermis by the basal membrane (a.k.a. basal lamina, basement membrane).

The process of wound healing in skin is extremely complex and obviously depends on the individual wound and how many layers are destroyed. There is a lot of detail on Wikipedia: http://en.wikipedia.org/wiki/Wound_healing.

If the basement membrane is not disrupted, there are two main components as a rule of thumb: 1) outwards-inwards migration, i.e. cells surrounding a wound will migrate into the wound. 2) bottom-upwards differentiation, i.e. the bottom-most layer contains replicating cells which will differentiate and squamify to regenerate upper layers.

Something like this (picture modified from Wikipedia): 

If the wound is bleeding, this means the basement membrane is disrupted and the dermis underneath is also wounded (the epidermis itself contains no blood vessels). In this case, the dermis needs to regenerate first, in a process which is probably similar as described above. Simultaneously, the bottom-most epidermal cell layer will proliferate to close the gap, and then deposit new basement membrane. Remember that the basement membrane is a mesh of proteins, not an actual cell layer.