Here’s a good information topic for MaxiGallery, check that:
http://modxcms.com/forums/index.php/topic,36851.0.html
There’s also a link to MaxiGallery wiki page, what you need to read.
To get the pictures open in a lightbox, define &display=`embedded` &embedtype=`slimbox`. But note that slimbox uses MooTools javascript library. If you have other javascript libraries in use, select a display type that uses the same javascript library. If you use quick edit in MODx, it uses jQuery, so slimbox won’t work when you are logged in to MODx manager. There is a guide in MaxiGallery wiki page to implement jQuery lightbox script.
Then Use &pics_per_page parameter in your maxigallery call to define how many thumbnails you want to show in one page and &pics_per_row parameter to define how many thumbnails should show in one row.
For example for your screenshot, it would be: &pics_per_page=`6` &pics_per_row=`6`.
Then create a custom galleryOuterTpl (seem maxigallery wiki page for the path of the original template). Create a new chunk based on the original one and change the maxigallery.pagenumbers part to the bottom of the template and modify it to show your images for next / prev links. Define your custom template chunk in MaxiGallery call.
Then I suggest you to take a look at creating square thumbnails using phpThumb in Maxigallery:
http://modxcms.com/forums/index.php/topic,41309.msg248965.html#msg248965
With that you can use phpThumbs zoom crop feature to tell it to create square thumbnails no matter if the pictures are land scape or portrait. The original images will still open in lightbox the way they are (but of course you could also use phpThumb for the original images too, to zoom crop them to square ones, if needed).
That should get you started.
