Cheat a lot. They point out some disassembly for you. ".ELF" is clearly some kind of magic string to confirm it's an elf file. "A4 00 00 00" looks like a 4-byte little endian integer (164) or perhaps an offset (0x000000A4 happens to be exactly where all the strings start), "34 00 20 00" might be a pair of shorts... 0x34 = 52 = "Start of program headers" among other matches - it probably corresponds to one of these fields! Try mutating the file and re-running readelf to see what fields change, or if the program still runs.
Just a hex editor and a way to correlate the raw bytes of the disassembly to where the occur in the file can get you surprisingly far. While there will be "dead" data that you can't determine the nature of, documentation can help fill in the holes once you start getting a hold on the "important" bits that actually do stuff (mostly make your program un-runable, I assume.)
