Where can the detailed requirements for EU Low Voltage Directive compliance be found?
The low voltage directive is, as its name suggests, a directive. It gives qualitative guidance as to what needs to be assessed to provide CE marking. Note that it is not the only directive, there is EMC and a good dozen of others which each have a scope. It is down to the manufacturer to identify, based on the directives scopes, which directives apply.

How can one prove that a piece of equipment complies to the appropriate directives, since each of their items is qualitatively defined? By the use of standards. Standards provide actual requirements for tests or reviews to be carried out on the equipment to certify. There is a number of standards out there*, but only those which are said "harmonised" and listed here for the low voltage directive, are authorised to assess compliance to the directives. Once again, these standards have even more specific scopes, and it is down to the manufacturer to select which one(s) to use. Sometimes, the customer will ask for a specific standard to be used.

*: Note that just about anyone could start a standard. However, it still needs to be recognised and accepted by the community (BluRay was launched by Sony for example), and in this context, harmonised by the european commission.