In Blender's Object Mode, all transforms are based on the object's origin, at least by default. You can control where the object is transformed from by changing the pivot point. The hotkey for changing the pivot point is the period key.

To transform an object more precisely, use snapping, either by enabling it in the 3D View header or by holding Ctrl while transforming. A separate type of snapping, called Snap Base, can also be used while transforming. The latter method is better for when you want to snap a component of one object to a component of another object.

Proportional editing (also called soft selection in other software) can be used to transform everything around the selection with a falloff. The hotkey for toggling proportional editing is O.

Want to learn more about Mesh Modelling? Check out the CORE Fundamentals on Mesh Modeling hosted by Jonathan Lampel