I don't mind saying, [b]cyanide[/b], but you were right: that is a crappy picture. However, it does illustrate the basic principle of a tie-back stabilization method. To expand on this a bit, the method involves a long rod that is drilled into the soil beyond the basement wall. Once the anchor is firmly bedded in the soil, a plate and nut are installed inside the basement, and the wall is stabilized from further deflection into the house. The science comes in knowing how many anchors are required, and wheter or not the existing basement wall has sufficient strength to withstand the repair. Furthermore, depending on the extent of the damage and subsequent repair, additional reinforcing of the wall may be required. This reinforcement may be in the form of strongbacks, walers or other structural elements.
Of course, this presumes that the the problem you are having is basement walls caving in. This is the most common problem with basement walls in regions with expansive (usually clay) soils. The basement wall as originally constructed was not provided with adequate reinforcing to resist the lateral hydraulic pressure of the soil.
The tieback method illustrated in [b]cyanide[/b]'s sketch only treats the symptom, in this case cracks in the basement wall. To prevent further damage to the wall, the soil in contact with the wall must be completely excavated to allow for installation of proper foundation drainage. Once the drainage is installed, the tiebacks can be placed and the excavation can be backfilled. It is essential to follow the engineer-specified backfill procedures for a complete repair. Finally, there will be continual maintenance in the form of landscaping and drainage to ensure that moisture does not build up along the basement wall.
Unless your local authority requires an engineer's seal on the drawings, you could just hire a qualified foundation repair contractor to design and install the repair.