For the most part,
Buffy is a straightforward action game in the vein of
Double Dragon or to some extent
Onimusha. At times, you'll run across a few basic 'find this key' puzzles, but a better part of the game is spent kicking the crap out of vampires and other denizens of the Underworld.
Storywise, the game is written as a lost episode after the third season and fits in really well with the rest of the Buffy continuum. For those out there who have never seen an episode of Buffy, the basic premise is that every generation one girl is born who has the gift of the Slayer. Once that Slayer dies, her power is passed on to another. As fate would have it Buffy, a high school cheerleader from the Valley, has inherited the Slayer powers. Speaking of fate, it also happens that Sunnydale, Buffy's town, was built atop a Hellmouth, which is a fancy name for a big rift in the ethereal plain that acts as something of a Mecca for all things unholy. For those who are still a little leery about jumping into a game that builds so much on the show, fear not because the game contains an excellent 'Slayer Files' feature to help get non-viewers up to speed as well as get viewers back into the third season mind set.
At the end of the first season, Buffy destroyed The Master, who is sort of the head honcho of all things evil. But as it turns out, you just can't keep a good demon down. The game opens up with the return of The Master and Buffy's quest to once again reduce him to dust. Although the story plays Tonto to the action's Lone Ranger, it's actually pretty good. I especially liked the in-jokes that were thrown in as sort of a wink to fans (the Xander/Cordelia moments are particularly amusing).
At first it may seem that Buffy is just another mindless brawl-fest, but it actually manages to bring a few bits of strategy into the mix and keep the game from becoming a bore. The combat system is everything gamers hoped The Bouncer would be and more. In addition to her normal punches and kicks, Buffy can string together combos (including her famous punch/backhand combo). By stringing together button combinations, she can also unleash Slayer moves which do a lot of damage, but drain Slayer energy. Performing these moves can be a bit of a gamble since many of them leave you wide open to attack for a few seconds if you are unable to connect.
One of the cooler things about the system is how well it merges with the game's environment. Nearly everything in each level can be used as a weapon in one form or another. Furniture can be broken and used as stakes, Vampires can be thrown into fires and burned, impaled on sharp objects such as fences, or tossed into the sunlight (in some levels you can even pull down curtains). Of course, Buffy also has her own arsenal including holy water, a (holy) water gun, and a crossbow. As Buffy progresses through levels she can even pick up random objects such as shovels, bats, and mops.
In order to kill an enemy, Buffy must stake him through the heart. Doing this is a hit and miss affair which requires timing. If she's able to catch a vampire off guard, she can easily stake one without breaking a sweat. However most of the time she'll have to wear a vampire down until the heart icon by his life meter is beating. After slaying enemies, they will release an orb of energy which will either fill up her 'Slayer Meter' or replenish health.