What is the easiest way to learn how to write Chinese characters?
Are Chinese characters made up of parts? Is there some easier way to learn how to write Chinese characters without having to study each one intensely?
Yes and yes. Study the recurrent parts (by which I mean any repeated pattern of strokes—not necessarily a radical). Comparatively few characters have constituent parts that are not widely shared with many others. All of these parts comprise strokes written in a (largely) predictable order, so even the most complicated character can easily be broken down into familiar components and written correctly once you have familiarised yourself with them (true, a handful, e.g. '龜', defy classification in this way and just have to be learnt).
James Heisig's books (T, S) essentially follow this method, and might be helpful to you (they are no help with remembering pronunciation, however, and his English 'key-words' can be rather arbitrary and/or misleading to the uninitiated).
just enjoy learning new characters, once you've learned the stroke orders of a few most of the others will come naturally to you, and chinese calligraphy is a great way to pass time if you have any time to pass(I have though)