If you'd like more historical information, try Andy Anderson's A Brief Background to Border Morris Dancing (or better yet, buy his booklet!). Or take a look at John Kirkpatrick's articles about morris dancing - I enthusiastically agree with (almost) everything he has to say.
Style: I'll be describing Border as the Hounds do it. You'll want to come up with your own "team style". Doing so is an evolutionary process - when you come across ideas that you like, incorporate them. Feel free to alter the dances as you see fit, and to incorporate gratuitous spins, yells, stick twiddles, etc.
Stepping: The Hounds do a simple relaxed single-step: left-hop-right-hop etc. You can choose a more energetic stepping style (e.g. lifting your knees high, or stomping into the ground) or a more complex style (e.g. the "Shropshire Bedlam" stepping - | L H R H | L R L H | R H L H | R L R H |.) Border stepping does not have the ornate movements (e.g. galleys) of the Cotswold morris.
Music: As I've notated it, each part has 16 beats. The Hounds dance at about 60-80 beats per minute.
Safety:
If you'd like more information on Border Morris, check