Each word has a clue, like a crossword puzzle. And like in a crossword puzzle you can use other clues you've figured out to help with the ones you're stuck on. The second two words in each typically go together, and may have a common theme, but the first pair of words is usually unrelated.
If you have some of the words, the puzzle will show which unused letters are left; click the little shuffle icon next to the letters to rearrange them and perhaps generate ideas.
If you just want to find some anagrams (or cheat a bit on these :-) you can try our online Anagram Finder.
For this group of puzzles, the second pair of words all refer to folk you might find up on Mt. Olympus.