First of all, in order to select the different expressions you have to create a 3D "character file" with Clip Studio Coordinate (CSC). The different facial expressions are created with a multi-layered PSD file. CSC is actually free, but has only been officially released in Japanese. See my info on how to apply the unofficial English translation to it and get the (Google auto-translated) version of the User Guide.
At a bare minimum you need to have layers for the expressions for Normal, Smile, Angry, and Sad. Each of these needs to have the following structure:
Expression (name of expression, Normal, Angry, etc.)
base ←should be a layer with the same as JPG texture mapped to head model
Then turn set the default eye/mouth combo for each expression. You can create additional expression presets either by adding a new layer for each of them into the PSD file OR you can duplicate one of the base expressions in CSC and then customize the name and default eye/mouth settings.
When you import a face/head in Clip Studio Coordinate it will automatically create placeholders for each of these basic expressions (these placeholders cannot be deleted).
Then you need to IMPORT your face texture/expression PSD file with the button in Face->Expressions panel.
In CLIP Studio Paint each of the expression presets appears in the selection box when you click on the little "face" icon below a model on your canvas:
Note that if you import a face/head model that doesn’t have any textures mapped on it you won’t be able to import an expressions PSD file until you map something to the head model!
You can do this in CSC by clicking on the model in the “Face” panel, which “un-grays” the empty “m_face_uv” texture in the “Textures” panel. Click on it and it opens a file dialog asking where the JPG texture is to map to the head model. Once you do that, THEN you’ll be able to click the “Import” button for the expressions PSD file. The easier solution, though, is to just map an image to head model when you create it in your 3D modeling program. Head models can only have ONE texture file assigned to them in your modeling program. CSC will import models with multiple textures, and show them in the Textures panel, but will inform you it can only use ONE of them. So best practice is to make sure your head model base texture is one image file.
If you want the nice little thumbnail images of each expression you have to (tediously) set each one in turn and use the little “Camera” button to take the thumbnail image. This makes it a lot easier to see what you're selecting if you want to customize the eye/mouth setting in the Tools palette once you're working in CLIP Studio Paint:
Once you’ve set up your character in CSC you save it in the Celsys proprietary “.c2fc” format. You can drag-and-drop this file into your canvas just like any other 3D model. If you want the model persistently available in your Materials palette, just go to “Register Image as Material” and assign it to the 3D->Character section.
Note: If you're on a Mac, dragging and dropping the model onto the canvas can be confusing because every time you click on the Finder window it will automatically hide Clip Studio Paint/Manga Studio. What you have to do is select it in the Finder, switch to CSP/MS and move the Canvas window so you can see the Finder window underneath, then drag and drop the already selected model file onto the canvas without actually switching focus to the Finder window.