Shutter speed is a measure of how long your camera's sensor is collecting light - the exposure time. It's a fairly simple concept - a long exposure allows more light to reach your sensor, and a short exposure lets in less.
Unless you're shooting in low light, it's actually pretty simple to master shutter speed. Though you can usually estimate exposure time in Shutter Priority or Manual mode, I just like to switch my dial to Aperture Priority and put shutter speed on Auto.
This allows for some level of creative control, but your camera will always deliver the 'proper' exposure and an acceptable shutter speed. In fact, getting your shutter speed right is so simple (in most situations) that I rarely even think about it.
Shutter speed only starts to become an 'issue' in low light. Thankfully, you don't need to transition away from Aperture Priority mode. Try making your aperture as wide as possible, and, if that doesn't work, try raising your ISO. You should be able to achieve sharp photos in a matter of seconds.
But what if you want a slow shutter speed, to produce those incredible long-exposure effects with water and clouds?
Usually, I would recommend using an ultra-dark ND (Neutral Density) filter to effectively trick your camera into thinking it's nighttime. If you don't have a filter, though, you can still produce the flowing-water effect by setting your aperture to f/22, your ISO to 100, and shooting away.
That should give you a shutter speed of at least a half-second, but depending on your conditions, you could end up with a 5-second shutter speed and an even better shot.