Your camera offers a lot of settings to make shooting easier. While I’m personally a fan of Aperture priority mode (where you set the depth of field and let the camera do the most of the rest) I also find Shutter Priority (or Time Value) Mode quite useful. In this shooting mode, you tell the camera how long to leave the shutter open. It will then determine the Aperture and ISO sensitivity. This is all part of shooting with the exposure triangle if you need a refresher.
Here’s a simple example with a spinning industrial fan. This photo is being used for technical illustration purposes (not artistic).

Here’s a gallery so you can inspect the images in greater detail.

You’ll note that as the depth of field in the scene increases, the shutter speed slows down. This is because more light needs to enter the camera to balance the exposure. This essentially streaks the action. Hence the fan blades become full of energy and motion. With the shorter shutter speed, the blades appear to freeze mid-rotation.
Here are a few more shots that use shutter speed to achieve the desired result.
A 10 second exposure turned the traffic in this shot into streaks of light.
Using a short shutter speed was necessary to capture this bald Eagle. Since the bird was moving a fast as a car, it was necessary to use a short shutter speed to freeze the motion. Look closely at the water droplets and point of impact on the water’s surface.
While this image is a HDR file made from multiple exposures (learn more here), I did use longer exposures to blur the water. This turns the water into a silky ribbon.
The use of shutter priority is a natural complement to shooting Aperture priority. It lets you control the amount of blurring in your exposure, especially when you want to drive the focus (or lack of) as a major part of an image’s narrative.