Hammer Editor - Making Animated Props

Create a prop_dynamic and find the world model you'd like to use. While the model browser is open take note of what it listed under the Sequences tab, this lists the animations the model can use.

When you find the animation you'd like to use go into the prop_dynamic's properties and find the property named Default Animation. In its text field enter a sequence name from the model browser, in the example below I'm use 'idle', which is found in the sequence tab in the screenshot above.

Compile your level and your prop should now be animated.