If you’re not already familiar with Force Touch, it’s essentially a hard press. Force Touch (or press hard) on the Watch screen and you'll be rewarded with a light buzz and a gallery of alternative faces for your Watch. From there you can then swipe through a myriad that are available to you.
Some of them are customizable, and are indicated by the Customize button at the bottom of each. Tap into those to tweak the respective Watch face's different elements to your liking.
To get to Glances - the Apple Watch’s equivalent of widgets - just swipe upwards on the Watch face to bring them up. You can then swipe as usual to get through them. To decide which Glances you want (weather, music controls, battery life, etc.), you can select or deselect them via the Watch app on your phone.
When there’s a red dot at the top of your Apple Watch face, it means that you have awaiting notifications. Just swipe downwards on the screen to view them. Tap on each to see more, and then tap Dismiss to send them hurtling into the black hole of dismissed notifications.
If you think the motions are similar to what you experience on your iPhone with notifications and the control centre, you're right. Apple has deliberately kept interactions as familiar as possible.