If you really want to apply direct to a gallery or curator, bear the following in mind:

• Find out the name of the curator or director and write directly to him/her.
• Print images on paper so that people can see them without any technology, or send a website URL
• Label each image with the name of the piece, dimensions, materials, and year made.
• Get someone else to write some text about it, rather than doing it yourself
• If sending writing, make sure it is by someone the curator might have heard of - art critics can be sent work and invited to exhibitions to write reviews, which may not be published but could be used in applications.
• Avoid writing about the content of your work - it is the job of the curator to decide what it is about.  A short paragraph about sources or theory that may not be noticeable in the work is permissible.
• Keep your overall style is clear and concise
• Address the pack to the correct person in the gallery
• Include a stamped addressed envelope if the contents are to be returned - but do not expect them to be
• It is infinitely better to ask a curator to come to your studio to see your work than see reproductions of it. If you do not have a studio, ask them to your house or wherever your work is stored.

This site also has an overview of writing applications for funding to companies and charitable organisations.
 

• getting an exhibition
• meeting curators
• exhibiting
• working professionally
• networking