Very important - no point logging the data if nobody can ever see it.

One way to do it is to just have it pour out of a serial port as human-readable ASCII text - rather like the "verbose" responses from a modem (OK, RING, ANSWER, CONNECT, etc). This has the advantage of requiring no special hardware or software to retrieve the data - even a dumb terminal will do. The disadvantage is that the embedded processor has to do all the formatting work.

An alternative is to still use ASCII text, but just have numeric codes - like the "terse" responses from a modem. This has the advantage of being much easier on the embedded processor, whilst still being accessible (just) to a human operator with only a dumb terminal.
You could, of course, provide PC software that would do all the fancy formatting & nice presentation to make it "operator-friendly"

A further option is to provide a pure binary dump. This has the advantage of being easier still on the embedded processor, but is now inaccessible without special equipment (eg a PC with the right protocol and/or decoding software).

Yet another option is to simply have the information logged in non-volatile memory, and have a test fixture that reads the memory directly (eg, via JTAG). This has the advantage of requiring no overhead at all in the embedded code for reading the logs, but means that it is totally inaccessible without the special test fixture.
This might be appropriate if the information will only ever be used when the unit has been returned to the workshop for repair, etc.

Of course, you might come up with a combination of them all - simple info is available in human readable text, advanced info just as codes, more advanced info in binary, and the real nitty-grit stuff requires the test jig.