Alexander LaVelle Harris was born and raised in Sunnydale, and was friends with Willow Rosenberg even in childhood (they used to sleep over at each other's houses regularly). Jesse was Xander's other best friend, until he was turned into a vampire and inadvertently staked by Xander, therefore turning to dust. As with most of the characters, not much thorough information can be found about Xander's family, except that his mom can't cook, there's alcoholism in the family (he sleeps outside on Christmas Eve to avoid his family's drunken fights), he has an Uncle Rory, and Cordelia has implied that his father is unemployed. Despite his problems (or perhaps because of them), Xander consistently maintains his sense of humor, making wise-crack after wise-crack, bringing levity to often-times angsty occasions. Xander was not an exceptional student, but he's always ready and willing to help Buffy in her endeavors.
His track record in the romance department has been less than optimal — he was turned down by Buffy, fell for a hot teacher who turned out to be a praying mantis, had a thing with an Incan mummy girl, had a one night stand with rogue slayer, Faith (only to be kicked out afterwards and assaulted by her not long after that, and would have died if there had not been intervention), attended the prom with an ex-demon, Anya, who he later left at the altar because of his overwhelming fears of turning into his father. During his strange but rather great relationship with Cordelia, he messed that up by kissing Willow ... and getting caught, and then Cordy got impaled and hospitalized, which did not help matters.
Xander did manage to graduate high school, although didn't go to college with the gang, instead tried this and that (e.g. ice cream truck man), before successfully turning to construction, where he both made pretty good money and was good at it.
After Tara's death in season six, Willow went all evil and turned dark side. Endowed with immense magical powers, she attempted to destroy the world. Although Buffy was no match for her, Xander managed to get through to his long-time friend by reminding her of their friendship and love over the years. Xander thus saved the world. One of the many times actually (watch The Zeppo for one, eh?).
Xander helped out Buffy with the First Evil in season seven, losing an eye in the process (eerily, in season six he played a pirate wearing an eye-patch for Halloween), and his jilted, but still loved, Anya, in the process. However, we later learn in Angel that he is recruiting slayers in Africa and is probably living a pretty rewarding life. :)
Andrew Wells is the younger brother of a character seen earlier on the show, Tucker Wells, who summoned demonic dogs to attack the high school prom in season three (The Prom). Andrew himself has skills in demon-raising and animal control, although these were not really used after season six. He credits his brother with giving him the courage to develop his talent. At some point during Buffy's senior year, Andrew summoned Winged Monkey Demons to attack the school's production of Romeo and Juliet, apparently for no other reason than to amuse himself.
Andrew joins up with Warren Mears and Jonathan Levinson in season six to form the Trio (or Troika, or "Them Three Nerds" if you like) to take over Sunnydale. They are thorns in Buffy's side throughout the season, at first rather comical and blundering. But as their plotting progresses, things turn darker. People get hurt, die, and situations become very twisted. Andrew and Jonathan become the only ones of the trio left alive after Warren is skinned (alive) by Willow, and she becomes bent on coming after them as well.
The scoobies help out, trying to keep them alive, but more for Willow's sake rather than either Andrew's or Jonathan's. However, Andrew and Jonathan think being far, far away is a good plan, and want to get the heck out of dodge. They make their escape, even pulling a sword on Xander in order to get away. After they do so, they head to Mexico. They both come back the next season, and Andrew, being led along by The First Evil, kills Jonathan as a sacrifice.
Some time afterwards, Andrew runs into Willow and is then taken to Buffy's house as a captive. He is tied up, questioned, and as time passes, he's seen to be more harmless than when under the thrall of the First. He becomes a fixture in the Summers house (writing/drawing on white-boards, trying to cook funnel cakes, running his video camera and narrating, etc.). When it comes down to it, Andrew fights side by side with Buffy and the gang. And he survives.
He's also brought back on Angel (Season 5). He's studying to be a Watcher under Giles. He's got slayers to train, and a slayer to collect in Los Angeles. And Xander, we find, is in Africa, and had even sent him an Mbuna fish at one point.
One of the big things that we learn is that Andrew leads a rather swinging social life. Who knew? :)
I think that though there is much antagonism and a certain tenseness between Xander and Andrew, there is so much geekiness and heart. I also really think they are on an even playing field, somehow. When Andrew freaks out when Godzilla (the Matthew Broderick remake) is mentioned, he whines to Xander, who immediately understands and feels his pain (in a totally geeky way).
They just get each other, and there's a lot of potential for a fantastic and long-lasting friendship. The antagonistic aspects are also appealing, as we all love seeing two geeks bicker and be agitated, and yet be on nearly the same wavelength. And in the end, there's also potential for something more, if you know what I mean. ;)
I just love them. And if you're a fan, you should really join the list. :D