The poem begins with a description of the setting – an afternoon, with strange, nonsense-creatures ("borogoves" [3], "raths" [4]) milling around and making noises. Then, we have some dialogue. A father tells his son to beware of something called a "Jabberwocky" that lurks in the woods and has horrible claws and teeth. There's also some other nasty stuff out there – the "Jubjub bird" (7) and the "Bandersnatch" (8). The son takes his sword and goes out looking for these creatures, and finally finds and kills the Jabberwocky. Upon returning with the creature's head, the father is overjoyed and they celebrate. The first stanza repeats, and things appear to return back to normal.
See? It's a simple tale. Just don't get too hung up in the badger-corkscrews (more on them later), and we'll be OK.