Taking a shot with this style of lighting is actually easy - timing the lightning and dealing with lions - not so easy :-)
The trick is that with a bright background if you expose for the background the foreground will be completely dark - but you can brighten the foreground to the same level with your flash (because you control the flash power you can control the foreground light level and the flash has limited range so it has no effect on the background).
First you choose your aperture for the depth of field you want.
Than you set the shutter speed so the background is well exposed, ignore the foreground for now (just keep the shutter speed slower than your max sync speed).
If you use a TTL flash you get just take the picture and the camera will do the rest, if you use a manual flash keep reading.
Set your flash power, you can choose the initial power based on the guide number (f number * distance = guide number at ISO 100 full power) guide numbers are not accurate but after doing this a few times you should know how to adjust your power.
If you have a little bit extra time you can, instead of messing with math, start from some middle-of-the-road setting and adjust from there (with my flash unit I start with 1/4 power).
You can use an higher ISO to conserve flash power, if you can't get enough power you will have to adjust your aperture (shutter speed has no effect on flash).
Also, flash attachments (umbrellas, softboxes, etc.) all waste some light, if you get to know your equipment you should know how much light each of your specific flash accessories wastes and use that knowledge to adjust flash power.
I can usually get everything right with 2-3 test shots (I'm not an expert like whoever took the lion shot).
This is quick and simple if you are photographing a model, maybe too slow if you are near a lion.