Drilling Piers under exterior wall
You haven't said what the foundation (referred to as a "beam") is built of. A poured foundation can span gaps of several feet temporarily. A block foundation may be supported by adequately reinforced footings. A temporary beam carrying some of the load on the floor joists could also be employed. 

As to how... a shovel. Despite our many evolutionary regressions due to over-
abundant modern conveniences, we're still able to grasp and manipulate simple tools fairly effectively. 

It's also possible that a backhoe could cut in from outside the foundation and bore underneath.