Start with What You Have

"What kit do I need?" It's our eternal question, isn't it?

Most of the time, I tell people to just pick up their camera and get on with it.
However: this is one of the few times when, realistically, you do need a couple of bits of kit.

In a studio, the most important additional thing is a background. This can be a plain whitewashed wall (and you'd be surprised how small an area you actually need) or a muslin, paper, etc.

As for light: a window (in the right weather) gives a lovely light, and a reflector positionned opposite the window can do a nice job as a fill.

If you've already got multiple lights and modifiers then I reckon you're more than well-enough equipped to get going. Once you've done one or two shoots, you'll soon work out if some additional kit would help.

For info: I have been working in an occasional "home studio" for a while, with a muslin background, 2 strobes on stands with umbrellas. Sometimes I'll add one or two reflectors. I've had some nice results, but I could really make good use of a couple more strobes.

Scott Kelby has some nice tips for a small studio in his Digital Photography series.

This may be relevant: Strobist.com has a great series of tutorials on getting started with small-flash photography.

PS. I'm happy to talk makes and models, but you didn't ask for that so I've left out all the gory details for now. :)