This one is complex and simple at the same time.
Professional Photographers that use a lot of lighting will tell you to expose for the elements that you cannot change – which is usually the background. The way that you do that is to spot meter the background, then spot meter the object that you are about to shoot.
Set your camera in Manual, and set the aperture and shutter speed for the first set of readings that you did for exposing the background.
Now, take you light and set it for the f-stop that you got when you metered the object. For off-camera speedlights, you can simply use TTL flash triggers and let it handle the settings for you, as the camera will be shooting in Manual. I tend to like to see them underexposed by up to one f-stop to balance with the ambient light. For strobes, you have to set them manually, so set the f-stop on the light, and shoot it. Take a look at the photo and the histogram, and adjust accordingly if you need to.
If you want to adjust the exposure of the background, do it with shutter speed adjustments – not with aperture or ISO. To lighten up the background (overexpose), slow the shutter speed down. Cutting it in half, such as changing it from 1/200 to 1/100, doubles the ambient light, which is one f-stop.
To make the background darker, speed up the shutter speed, which reduces the amount of ambient light captured by the sensor.
The important thing to remember is that your object that you are lighting with either flash or strobe will remain the same – it is not dependent on the shutter speed.
If your background is exposed the way that you want it, you can adjust the lighting of the object with flash compensation. Simply turn the power up or down on the flash, and the lighting on the object will change up or down along with your changes.
The important thing to remember here is that flash compensation has no effect on the background exposure, as it is not being lit by the flash, only the ambient light.
Use shutter speed to control the ambient light for the background.
Use flash compensation to control the object(s) that you are lighting with the flash.