Updated for Blender Version: 3.1
To the Point
- Select the object.
- Ensure the object has enough vertices for the displacement. Press Tab to enter edit mode, select all and subdivide (ctrl+E > subdivide).
- Go to the Modifier Properties panel
and select “Displace” from the “Add Modifier” dropdown. - Press the “New” button to add a texture.
- Go to the Texture Properties panel
- Press “New” to add a new Texture, then click “Open”, find the displacement image and click “Open Image”.
- Go back to the Modifier Properties panel and adjust the Strength and Midlevel sliders in the Displace modifer as desired.
The Details
The Displace modifier is a great way to add a lot of details to a simple object without having to do a ton of modeling.
Set up the Object
In order for a Displace modifier to work, the object with the Displace modifier needs to have plenty of vertices. A single plane with no loop cuts would not be able to properly displace. Start by selecting the desired object. If the object needs more vertices, press Tab to enter Edit mode, then press A to select all vertices. Press Ctrl+E and select Subdivide. A small pop-up window should appear in the lower-left corner of the 3D viewport.
Use the “Number of Cuts” slider to adjust how many loops will be added to the object. With the Displace modifier, it is better to have more vertices rather than fewer.
Add the Displace Modifier
When you are ready to add the modifier, open the Modifier Properties panel , click the “Add Modifier” dropdown and select Displace. The Displace modifier takes a black and white texture input – darker areas on the texture will be lower, and lighter areas will be higher. Click the “+ New” button to add a new texture. If you already have a texture loaded in the scene, click the small checkerboard dropdown on the left and select the appropriate texture. If not, click the Texture Settings button 
. This will open up the new texture in the Texture Properties panel. From there you will be able to add an image texture, or create a new one.
Your object will likely look like some crazy mountains. That’s ok. Dial back the strength a bit. Use the midlevel to adjust your object up or down to get back to where you would like it.