Sounds like what you need is a solid evening spent reading the Strobist blog! It really helped me understand the principles of lighting with strobes.
There are 4 things you can do to adjust exposure. First is strobe power, which you can control by a knob on the strobe, or by moving the strobe further away, etc. Second is ISO, but usually this is used when you want a lighter shot, but if you are shooting with a high ISO, you can drop it down nice and low for macro work, such as iso100.
The next thing is shutter speed, which when you are using a strobe, really controls the "background" or ambient light in the shot.
The last thing is aperture. The reason you control the strobe light by aperture and the ambient light with the shutter is due to how fast the strobe fires. Lets say that the sun is throwing 100 units of light per second at your camera. So, by a half second exposure, you get 50 light units. The sun is constant as far as the camera is concerned, so you control the portion of light from the sun by changing how long the shutter stays open.
However, strobes fire super, super fast, lets call it a thousandth of a second. So, if your strobe fires 100 light units, and you have a half second exposure, as long as the strobe fires during that half second, because it fires so fast, all 100 light units will get in the camera.
It sounds like you aren't using TTL, since then your camera should quench the strobe and keep your exposures decent. If you are shooting manual, it is not uncommon to shoot with a shutter speed of 1/60 to 1/125 (if your subject moves or is blurry, try to go faster, if you want the background to be bluer from natural sunlight, you go slower) and an aperture of f16, 18, 20, 22, etc. Today, I was shooting at f32, with my strobes on full. It all depends on the situation.
Your camera should be able to fire a few test shots on land without harming the strobe. It can overheat if you shoot too rapidly, just like any strobe or speedlight. Set up in a dim room some kids toy or something, and try taking some pictures to practice.
Lastly, shoot in raw if at all possible. It won't fix truly over or under exposed pictures, which contain no data at all in those pixels, but it will let you fix minorly off shots.
