1. General: The Wikipedia article here provides an accurate overview.
2. Maintenance: "General Inspection And Maintenance Of Gutters And Downspouts". Available on the website of the US General Services Administration.
4. Technical: Gutters and Downspouts: Sample Gutter Sizing Calculation can be seen at the website of the Copper Development Association, and walks you through the process of determining the proper dimensions of a hypothetical gutter. (Table 4.4.2 - Rainfall Data and and Drainage Factors is viewable here).