How do you use a fuse with a rating of Amp-Hours?
The short answer is that if they both have an 8A in their name then they can replace each-other. The details of the fuse are important if your supply can source very high currents(100s of amps) or if you need to deal with issues such as irregularly but short current trips that should not cause a fault.

What does the H mean?

The confusion comes from fuse nomenclature. It is not surprising either as my google fu did not easily return a list of what identifiers refer to. 

This document points me to a useful table though. It seems as thought that 'H' refers to the maximum current that the fuse guarantees it can interrupt.
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Omega's document on fuse selection that I mentioned previously has quite  a large amount of information to learn from if you would like to learn more about fuses. Choosing a fuse to protect circuitry without faulting regularly for no reason is something EDN and Electronic design magazine have had good articles about.