Well, Alaric marched on Constantinople in 395, the date I picked for the POD, and, unable to take the city, decided to attack Greece instead.
Hmmm, how about this for specifics:
Alaric advances on Constantinople. Upon seeing the fortifications, he knows that he cannot take the city by force. Luckily for him, somebody on the inside lets him in. We'll never know who this was, as every faction in the city accused their enemies of the deed, so there exists no unbiased account of the event.
So, with the fortifications bypassed, the Visigothic army takes the city easily. Alaric then turns Arcadius into his puppet, not too hard to do. Arcadius was basicly controlled by Rufinus, his guardian and the Preatorian Prefect. Luckily for us, Rufinus didn't happen to be in Constantinople around this time. Which means he escapes capture and certain death. Which means he can rally Roman opposition to the Visigoths. Oh, and did I mention that he and Stilicho (his western counterpart) hated each other with a passion? Heh, this is good stuff.
So, Alaric then invites every Germanic tribesman willing to prove his loyality to the eastern empire, as federates. They readily take him up on his offer, since they trust him, a fellow barbarian, more than the Romans. Can you say Volkswandering -whatever the german word for east is- ?
Sadly, I don't know a heck of alot about them in particular. Besides, all those barbarians all look the same to me...