Perceptual Mapping Overview
Broadly speaking, positioning is the process of developing a competitively distinctive set of customer perceptions regarding a brand or product. That is, getting customers to internalize an understanding that a product is different from competitive products and closely matches their buying criteria.
Customer perceptions are the acid test of whether benefits are delivered. A product may meet objective performance criteria (e.g. can be validated by laboratory tests), but a company only "gets credit" if customers perceive that the product delivers the benefits that they are seeking.
In other words, meeting the objective performance criteria is necessary but not sufficient. Assuming that a product is designed to the proper market-driven specifications and "made to spec", non-product Ps - especially promotional elements like advertising and other customer communications - must operate to close any gaps between positive realities and customer perceptions (i.e. customers are unaware that a product delivers a specific benefit)
Analytically, the primary positioning tools are called perceptual maps. Perceptual maps, which can be derived using market research methodologies such as semantic and multi-dimensional scaling, are based - as the name implies - on customers perceptions of the benefits that brands deliver. The maps are visual representations of competitive brands (or products) plotted along dimensions that capture the most important attributes in the purchase process. The maps reveal brands' positions relative to each other, and relative to customers' ideal points.
For example, the illustrative perceptual map below plots brands (the letters in squares) along 2-dimensions: price and quality.

Brand A is perceived to be relatively high priced with high quality; brand F is low quality and low price (perhaps an economy brand); and brand G is in the unstable position of being perceived to be low quality, but high price. The circled numbers indicate the ideal points - combinations of price and quality - that are desired by each of 3 illustrative segments (good, better, best). Since price is along the vertical axis, this perceptual map is a variation of a value map.
Proximity rules on perceptual maps. In general, a brand will accrue most of its sales from the market segments with ideal points closest to where the brand is positioned (e.g. brand A is likely to draw most from segment 3) and, all else equal, brands positioned closer to ideal points will capture a disproportionate share of that market segment's sales (e.g. F should outperform C is segment 1).
Strategic & Tactical Implications
Of course, customer perceptions may, or may not match the objective realities. Meeting the objective performance criteria is usually necessary but not sufficient. That is, a product may meet objective performance criteria (e.g. can be validated by laboratory tests), but a company only "gets credit" if customers perceive that the product delivers the benefits that they are seeking.
Assuming that a product is designed to the proper market-driven specifications and "made to spec", promotional programs, like advertising campaigns, may be required to:
(a) Close any gaps between the favorable positive objective realities and inaccurate customer perceptions
(b) Amplify the perceived importance of any attributes on which the brand is competitively closest to customers' requirements
(c) Diminish the perceived importance of any attributes on which the brand misses customers' requirements.
Market Research Methodologies
A variety of market research methods are used to compile perceptual maps. The primary techniques are semantic scaling, multidimensional scaling, and conjoint measurement.