I'd like to convert a room downstairs into a home studio to do mostly portrait/fashion/pet photography. I have a few strobes, softboxes, and stands, but that's it. What are the bare basics needed to get started?
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.
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. :)
I found Zack Arias' tutorial to be incredibly helpful, and extremely straight forward and easy to understand. I won't bother to regurgitate it here, I recommend you go read a bit.
The minimum equipment needed to take a decent picture is two light sources and a background, so either two lamps/flashes or one lamp/flash and a reflection screen.
The reason that you need a minimum of two light sources is that the images will look very flat if you have a single light source.
That is the bare minimum, everything after that is just to make the work easier. You might want more light, for example a separate light for the background, and a light meter can be very handy.
The basic minimum for flexibility and creativity are
The most expensive of these items is the 4x6 softbox - can run you $500+ for a very good one. Consider renting, or using a bed sheet as a scrim to diffuse the light.
With this kit, you will be able to do 90% of things and for the other 10% you should rent (e.g. ring flash).
You're probably going to want a background stand for holding paper or muslin backgrounds. You can acquire different backgrounds over time to suit your needs. If you don't need portability, you have more options about your background stand, e.g. you can make it yourself.