Every electron pair around the central atom is treated as a point charge on a sphere, and every pair pushes every other pair away with a repulsion that falls off with the square of the distance between them. Nothing here is told where to sit: the shapes you see are what that repulsion settles into on its own. Bonds also have a length they prefer, so an atom pulled in or out springs back.
Drag any outer atom (or any lone pair) and let go. The rest of the molecule responds while you drag, and the whole thing relaxes back to the same arrangement afterwards. Shake throws everything off at once, which is a quicker way to see that the geometry is a genuine minimum rather than a starting position. Drag the empty space to turn the molecule round.
The angles under Measured are the real ones, from experiment. For carbon dioxide, borane, methane, phosphorus pentachloride and sulfur hexafluoride the model reaches them with no help at all: equal charges repelling on a sphere give 180°, 120°, 109.5°, 90° and 120°, and every one of those is fixed by symmetry anyway.
The last entry in the row, AXnEm, is not a substance. Set any number of bonding and lone pairs, up to six between them, and the model builds whatever those pairs settle into — including the see-saw, the T-shape and the square plane, which need five or six pairs and are easier to believe once you have watched them form. Where the lone pairs go is not written down anywhere: the model costs every arrangement and keeps the cheapest. Nothing here has a measured angle to be checked against, so that column reads as a dash.
Ammonia and water are different. A lone pair sits closer to the nucleus than a bonding pair and is not pulled towards a second atom, so it takes up more room and presses the bonds together — but nothing in the model works out how much more room. That one number is set by hand for each molecule, to whatever reproduces the measured angle: 107° for ammonia, 104.5° for water. It is worth knowing which of these shapes the model predicts and which it has been told.