In terms of f-stops, how much light is typically lost when shooting through an umbrella?
That's going to vary a great deal depending on whether it's a bounce or shoot-through, what material is used, etc. In general, the range can be as little as 1/2 stop (or less) through to several stops. If you're interested in a particular brand, you can probably find details on light loss in the product literature. Lastolite, for example, will supply the light loss information for their umbrellas.