The h itself isn't pronounced at all. When following another consonant it represents a new sound. These new sounds are different kinds of fricatives depending where and how they are formed.
The aspirate h in French is one that appears in the written form but is not pronounced but prevents a liaison with the following consonant e.g. Les Halles pronounced [lay al] not [layzal].
In English the aspirate h is pronounced as in history, Hampshire, hurricane, etc in RP.