This add-on now requires 2.8x. I might consider redesigning the add-on to have a better UX if it becomes popular. It was mostly something that I hacked together to solve my use case.

1. Download mesh_makecoplanar.py from this repo (ex: by clicking the Clone or Download button and clicking Download Zip).
2. Open Blender Preferences with Edit -> Preferences.
3. Click the Add-ons tab (on the left).
4. Filter your add-ons to only show Mesh by clicking on the filter drop-down (below Official) and select Mesh.
5. If Mesh: Make Coplanar exists with an author Scott Michaud, click Remove to uninstall the old version.
6. On the top right, click the Install... button.
7. Navigate to where you downloaded mesh_makecoplanar.py and Install Add-on from File....
8. Click the checkbox (square) to the top-right of Mesh: Make Coplanar.

1. In Edit Mode, select 3-or-more vertices.
2. Either:
   1. Press the space bar and type "Make Coplanar". OR
   2. Press Ctrl + V (Vertex Tools Menu) and select "Make Coplanar"
3. The desired plane to move vertices to will be calculated:
   1. If 3 vertices were selected, it will be the plane that they form.
   2. If 4+ vertices were selected, an average plane will be calculated. These vertices will be moved onto it.
4. Your vertices will unselect.
5. Select more vertices to align with that plane.
6. Press Enter to move this second selection onto the plane, or ESC to not move the second selection.

There are two common use-cases:

1. If you have a bunch of vertices that are not coplanar, then select the vertices that closest represents the plane that you are trying to model and run the command, then select the outliers to conform them to the same plane and press Enter.
2. If you already have a plane, but you have some vertices that fell off of it, then select 3 vertices from the plane and run the command, then select the outlier vertices and press Enter.