The number of methods and procedures for developing solution ideas is almost innumerable, and these guidelines are a fertile bunch, constantly multiplying. This chapter serves as a “compass” to practical methods of idea generation. It succeeds in breaking down the invention process into basic elements that form the building blocks of methods and procedures—similar to how elementary mathematics is based on the four basic arithmetic operations of addition, subtraction, multiplication, and division. The “basic arithmetic of invention” are analogy, variation, and combination supported by the central element, dialogue, and linked through abstraction and concretization. The analogy method, the variation method, and the combination method are described in detail and illustrated with clear examples. The deeper analysis of the methods provides the basis for their computational implementation.