Table 2.8 gives quite approximate formulae for converting from pixel number to an astronomical coordinate. For more accurate formulae, see AIPS Memo No. 27, ``Non-linear Coordinate Systems in AIPS'' (Eric Greisen).
For example, the following code fragment calculates RA, DEC and velocity.
This code fragment checks that the axis are in the order RA, DEC then velocity (i.e. the normal ordering) and aborts if they are not. Smarter code would allow them in any order, and would probably treat any unrecognized ctype as a linear coordinate system. It uses default values (if values of crval, crpix and cdelt are missing) of 0, 1 and 1. Probably better default values could be chosen, though if ctype is an item, then we can be fairly certain that the other parameters will also be present.