Each time I'm asked how its done I try and improve my explanation...
Two MTF charts. Carl Zeiss 2.8/21 Distagon T* MM. Details at 10mm^-1, 20mm^-1, 40mm^-1.
The Y axis (the information) is the sharpness of the rendition of the lens, measured as the fraction of subject contrast reproduced by the lens. The X axis is the distance from the center (along the radius) in mm. Points of interest for 135-format sensors are the edge at 18mm and the corner at 22.5mm, and for APS-C (1.5x) sensors the edge at 12mm and the corner at 15mm.
An MTF chart usually comprises 2 or more pairs of curves. Each set plots the contrast for a different size of detail that’s being projected by the lens. Smaller-sized details always reproduce with lower contrast than larger-sized details.
Solid and dashed lines
The solid line is for radial details, the dashed line is for tangential details. Lenses will often not resolve details exactly as well in both directions. e.g. at the border a vertical line might look sharper than a horizontal one, or vice versa.
Often the tangential details (concentric rings radiating from the center) don't do as well as radial details (lines radiating from the center). When the solid and dashed lines are far apart (say more than 20% contrast difference) then the lens is astigmatic. In some cases the effect can be extremely unpleasant, see the articles on the 70-200/2.8 lens: 1,2.
MTF charts are a great way to compare the offerings of different manufacturers without racking up a massive credit card bill. But there are some subtle differences in the way each of the manufacturers report their MTF:
Nikon and Sigma charts have curves for 10mm^-1 and 30mm^-1 details at full aperture only. For zooms one chart is provided for each end of the zooming range.
To these Canon charts add curves for the same-sized details at two aperture stops down also. Note that Canon charts are theoretical, not measured, and so may be optimistic in the face of assembly tolerances.
Zeiss charts have curves for 10mm^-1, 20mm^-1 and 40mm^1 details 2 working apertures (like Canon). They are usually provided along with plots of light fall-off (vernacular: vignetting, though that's a misuse) and geometric distortions.
Leica extends the Zeiss charts with curves for 5mm^-1, typically describe 3 working apertures, and also come along with depth-of-field tables and charts. These are the most complete lens documents of any manufacturer.
Almost every lens on the market today has an MTF chart for you to look up. If a lens doesn’t, it’s very suspicious - Tamron and Tokina MTF charts are hard to come by, and I personally find this dubious. There are also isolated examples of "missing" charts from the big guys... like the Canon EF-S 17-85 IS, an infamous lens among review circles.