I'm used to taking pictures indoors using studio lights against backgrounds but what kind of settings do I need to use studio lights as the flash, inside the home where I would also like to include the surroundings in the image (rather than blocking out ambient light).
The main difference between shooting in studio, where you have total control of all of the light, and in another setting where you are mixing in the ambient light is that of the color of the different lighting sources. Your studio flashes need to be modified with colored filters to match the color of the ambient light. These are often referred to as "gels", even though most of them today are no longer made with the fragile gelatin material that was once very common.
As far as balancing the ambient and studio lights go, you control the amount of ambient light by changing the shutter speed. Since the flash is of a much shorter duration than your camera's sync speed, changing the shutter speed (Tv) won't affect the power of the flash(es). A longer Tv will make the ambient lights brighter, a shorter Tv will make the ambient lights dimmer. Changing the aperture or ISO will affect both the flash(es) and the ambient light(s) similarly. Changing the power setting of the flash will only affect the flash and not the ambient.
How you go about this will be determined by what variable you consider the most important. If you want a specific aperture for controlling the depth of field, then you would set the aperture first. Then, using your camera's flash sync speed for the Tv, set your flash power (and ratios) to get the desired amount of light from the flash(es). Then reduce the shutter speed until the ambient light is where you want it. If there is already too much ambient light at your camera's sync speed, then reduce ISO until the desired amount of ambient light is reached and then increase flash power until you regain the amount of flash light that you desire. If you run out of ISO and there is still too much ambient light at sync speed, then you must consider using a Neutral Density filter to reduce it further. This will also require an increase in flash power to compensate for the ND filter.
Use a longer shutter speed. The longer the time is that the shutter is open, the more influence does the ambient light have in the exposure.
You control the ratio of ambient to flash by the power setting on the flash or by adjusting the flash to subject distance. The distance adjustment method -- Know your flash's guide number. You can find this by test or from the flash's instruction manual. We use the guide number to set the taking aperture. Suppose the guide number is 110 and the flash to subject distance is 10 feet. We divide 110 by 10 = 11 meaning the aperture setting is f/11.
To answer your question: Meter the ambient scene and set the camera to that aperture. Now divide the guide number by this aperture value. Say the ambient f/number setting is f/16 then 110/16 = 6.9. This will be the distance in feet to place the flash to match the ambient exposure. Now multiply this distance by 1.4 the answer is 9.6 feet - this is the revised distance to set the flash subordinate by 1 f-stop. This sets up a desirable ratio (3:1) for the flash to becomes the subordinate fill. Want more contrast? Use 2 as the multiplier, this establishes a 5:1 ratio. Try this method you might like it.