The basics for shooting skate shots with strobes is to underexpose the ambient light by a stop or two using your aperture and then use your strobes to expose the skater properly at the iso & fstop your camera is set to.
So, roll up to the spot and set your camera's iso and then the shutter speed to your camera's sync speed (1/250th usually if you're using a 35mm slr type). Take a meter reading using the camera's own reflective meter or a hand-held incident meter. Say you get the following: iso100, 1/250th & f8 for a 'properly' exposed shot of the spot. Now close down your aperture to f11 or f16 or more depending on how dark you want the spot to look. Of course, if you don't want to use such a small aperture then bump up your iso so you can use a larger aperture.
Next, position your strobes and power them up to expose the skater properly at f11 or f16 or whatever f-stop you have your camera set to. Having a hand-held incident/flash meter helps get this done much quicker than chimping away in-camera but that works too.
It's all a juggling act because you are trying to overcome the ambient light at the spot with the strobes but as you power your strobes up to match the exposure, the flash duration lengthens. A short flash duration is what freezes the skater in the shot without any blurring from their movement. So you need to find out what the t0.1 (t0.5 will do in a pinch) measurements of your strobe(s) are at each power setting and don't power your strobes up beyond where t0.1 is longer than 1/1000 of a second.
If you find that you have to power up your strobe past the point where the flash won't 'freeze' the skater you'll need to add more strobes to the shot or wait till the ambient light starts to fade at the spot.
I haven't shot skating in about 16 years so I may be a bit rusty but the above is how I used to shoot
https://www.instagram.com/p/BhLvhuKB9bs/ Marginal Way in 2006 or so. Shitty flatbed scan of a 35mm slide.