You can change the channel various ways, depending on your device.
Web/Desktop: You click directly on any channel in the Channel Guide. You can either scroll with your mouse and click OR use the arrows on your keyboard to change channels.
Mobile: You can click directly on the channel in the guide, and in 'Full scree' mode, you can simply tap anywhere on the screen to bring up the channel options.
Roku and Apple Tv: You can use the proprietary remotes for those platforms.