Active measures

When handling mould affected books, always use gloves.
Source; http://www.disasterrestorationexperts.com/clean-up-services/mold/book-mold-removal/

While mould outbreaks are largely preventive some minimal mould cleaning is sometimes necessary. However as mould spores are irritants to the human respiratory system and can cause some health issues, individuals handling mould affected books should be protected by disposable rubber gloves, use clothes that can be disposed of or washed in hot water and wear eye protection and face masks. Masks labelled P2 offer better protection or even more suitable would be high efficiency air HEPA filtered respirators. Disposable gloves and dust masks should be disposed of safely in sealed plastic bags.

If a mould outbreak occurs, it should be dealt with quickly to limit damage and prevent contamination of other materials;

1. Mould affected books should be isolated in a dry place prior to treatment. This should be done with care so that mould spores are prevented from spreading.

Similarly protective gear should always be worn if dealing with large outbreaks of mould.
Source; https://www.nedcc.org/free-resources/preservation-leaflets/3.-emergency-management/3.8-emergency-salvage-of-moldy-books-and-paper

a. If items are already dry, you can steal them in plastic bags until treatment to prevent spores spreading.

b. If mould is damp, the book needs to be removed to a well-ventilated isolated area, with waste paper protecting shelves while it dries. Fans are not suggested to increase drying time as they spread mould spores. Areas that have shared air-conditioning systems should also be avoided as spores can be dispersed using these systems to other areas of the institute. If materials feel cool or show evidence of moisture, they need further drying time.

2. When dry – the stage at which the mould is deactivated as should be dormant, and is dry and powdery rather than soft and fuzzy – clean the mouldy surface.

a. Use a HEPA-filtered vacuum cleaner fitted with a micro-vacuum attachment to reduce the level of suction so that mould spores can be removed gently.

b. A soft natural bristle brush can also be used to help remove spores. Brushing should be done carefully from the center outwards and always being mindful of tears in the book.For more on correct cleaning techniques.

c. Both treatments should be carried out in a fume cupboard to prevent the spread of spores and by someone who feels confidence to undertake the measures.

This person is merely cleaning a book, but cleaning mould affected books would be done in much the same way.
Source; http://balfourlibrary.blogspot.com.au/2011/08/balfour-library-conservation-project_24.html

3. Before reshelving, shelves need to be cleaned with hot soapy water, rinsed and allowed to dry completely. Identifying the cause of the outbreak (leaking pipe, shelf backed against outside wall) and taking steps to prevent it again is essential.

4. Ongoing monitoring of the affected books and area will also help to see if further mould growth might occur.
These steps are helpful for small outbreaks of mould. If large scale leaking and mould infestation has occurred or if HVAC systems have been infiltrated with active mould spores, contacting a professional conservator might be required as freezing of the collection is sometimes required and a plan needs to be formulated.