Install the zip file the same way you would any other blender add-on:

Preferences -> Add-Ons -> Install

Navigate to the directory where you saved the gridrigger_addon.zip file. Install & Enable with the checkbox.

Explaining the UI:

Resolution:

How many points to distribute across each axis. The influence of each point on the mesh will be distributed evenly according to their location in 3D Object space.

Mode:

If you have multiple objects selected, you can choose whether to rig them each individually, with their own "grid-rigs" or to create one big rig for the whole selection.

Hide Lattice:

Enabled by default. This will hide the root lattice driving the deformations when creating the rig.
Typical usage should not require viewing the lattice and I recommend leaving it enabled for a cleaner layout, but feel free to disable (either here or in the outliner)

Grid Rig It:

Create the lattice-based rig around the bounding box of your selection. 

Purge Rig:

Best way to delete old or unwanted grid rigs. Select the rig you want to purge and click purge. This should help keep your outliner/modifier stacks clean.

Extend Functionality:

The lattice modifier is still available in the object modifier stack(s). Feel free to mask the grid rigs influence using vertex groups, or apply certain poses as shape-keys or just totally break the tool!

UPDATE NOTES

v02: adding support for non-(0, 0, 0) cursor locations. (zeroes out cursor during build then returns it to initial location)

v03: attempting to fix installation issue for older Blender versions + moved the addon to its own viewport sidepanel tab "gridrigger"