Every museum has it's own policy regarding donations. However, they usually review possible donations on an ongoing basis. If the work you would like to donate seems appropriate for the museum's collection, contact the chief curator of the correct curatorial department. The museum will need to see high quality documentation of the artwork, the artist's resume and additional materials such as reviews and catalogues. When meeting with curators, tell them why you would like to donate to their collection and specify any special requests for the work.
When a museum accepts donated art, the work becomes part of the museum's "permanent collection." As the permanent collection is a continuously changing body of work, the donated work may only stay in the collection for as long as the museum curators deem it appropriate for the collection as a whole.
Museums tend to favor unrestricted donations, allowing curators to have complete control over the art. If you have restrictions, such as that the art never be sold, that it be shown within a certain time period or that it should be reproduced in catalogues in a certain way, specify them to the curator. The more important the art, the better the chances that restrictions will be honored. Donating art to a museum raises the profile of the artist and value of the artwork. Art dealers often give priority to collectors who promise to donate work to museum collections.
Make sure you understand the tax implications when you make a donation. A tax accountant or preparer can explain tax benefits to you and assist in filing appropriate tax forms.