Aphanitic rocks: These are classified by chemical, not mineral content. A large proportion of igneous rocks aren't suited for this classification method: The corresponding volcanic rock types are called rhyolitoids, but not very often. 
The middle three plutonic rock types - granite, granodiorite and tonalite - are together called granitoids. For plutonic rocks, gabbro and diorite have plagioclase with a calcium percentage (anorthite or An number) above and below 50, respectively. Which name to use depends on the composition of the plagioclase.
Notice that the rock names at the P vertex are ambiguous. That's the official definition of the fields, and you can calculate your rock's position that way too.
Notice that the lines that fan downward from the Q vertex are based on values, expressed as percentage, of the expression P/(A + P), meaning that each point on the line, regardless of the quartz content, has the same proportions of A to P. (Naturally, the number for A will also be there.) Read its name from the field in the diagram. The point where the lines for Q and P meet is your rock. That will be a line parallel to the left side. Measure along one of the sides, then draw a horizontal line at that point. Draw a line on the ternary diagram below to mark the value of Q, zero at the bottom and 100 at the top. Discard M and recalculate Q, A and P so that they add up to 100 - that is, normalize them. 
Determine the percentage, called the mode, of quartz (Q), alkali feldspar (A), plagioclase feldspar (P), and mafic minerals (M). In plutonic rocks, all of the minerals are crystallized into visible grains. The QAP ternary diagram is used to classify igneous rocks with visible mineral grains (phaneritic texture) from their feldspar and quartz content. (c) 2008 Andrew Alden, licensed to ( fair use policy) Igneous Rock Classification Diagrams Click the image for a larger version.
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