Character etymology is a great foundation for learning characters because it gives you an intuitive sense of the word. It can help you predict the meaning of unknown words in context and it can be a useful mnemonic for memorization. It can also help you "see correctly" the various character components of each character, which really helps with retention. Because I know most of the components, if someone flashes a not-too-off-the-wall character at me for just a second or two, I can generally transcribe it even though it's my first time seeing it.
I'm going to shamelessly plug my former professor, Larry Herzberg to get your started. A brillant linguist and a one-of-a-kind teacher, he's written a clever book with both silly character etymologies to help you with quick memorization as well as actual etymologies for each character he introduces. Honestly, he just penned down what he did in class every day - things like swiping one hand back and forth over the other like spreading mayo every time he said 没有, or pointing to his eye, then heart, then slapping his knee everytime he said 我爱你 - the man was gifted. Working through this book should give you the springboard you need to consider self stuy. Tools like www.yellowbridge.com and www.chineseetymology.org then become great resources for you to continue your investigation.
What I found useful was painstakingly grinding my first few hundred characters for their etymology, studying them as if I were preparing for a test. After about 500 or so, it gets exhausting and unfeasible, but you already have the foundation for character crunching because after this you will already "get" a new word when you see it, and if you don't a quick spot check will get you up to speed.
Honestly, after a while it can be a little annoying - "ah, this one's lost to time and space", "well this phonetic component is meaningless now", "simplification is so hideous (re: 体, see below)“, "so no one knows, eh?", "oh yay, another heavenly stem, wonderful" - but don't be discouraged, it's an amazing way to learn Chinese characters and can save you a lot of grinding with the pen and paper.
To actually answer the first half of your question, here's a copy-paste introduction of the basic types of character etymologies I did a long time ago:
Came to second the etymology method. Yellowbridge.com is a pretty good source. You should know there are five basic character compositions:
> Indicative
Usually the horizontal han stroke "一" literally indicating what the meaning is. In 下 it is below the horizontal axis, indicating the meaning; in 上, it is above it doing the same; and in 本 it is at the base of the tree indicating roots.
> Pictographic
The most obvious. They are just pictures. 山 are mountains, 木 is a tree, 口 is a mouth, and so on.
> Pictophonetic
This is the most common, where one half of the character indicates meaning and the other indicates sound. 毕 is made up of 比 and 十. 比 is for help with pronunciation, and 十 is a culturally significant number that means perfect or complete, indicating its meaning. 听 is made up of 口 for meaning and 斤 for a partial phonetic.
> Associative Compound
Here all the radicals work together to contribute to meaning. So the traditional character 聽 is made up of 耳,王,十,目,一,心, here creating the story that if the student (here: 王) uses his ears so that ten eyes can see that he is of one heart, then he has truly heard. 律 is walk 彳as it is written 聿.
Another possibility is where all of the individual radicals form together Voltron-style into a character that transcends the meaning of its constituent parts. Here is the traditional character 畢 for 毕. The bottom part is a picture of a net with a trap mechanism, and the top is a field. So the farmer takes his net into the field and once he's caught all the rabbits, he's finished or completed. And the character 業 (业) is simply a picture of a music stand indicating profession.
> Simplification
This is the final type of character composition. Simplified characters happen in three ways: 1) skeletal outline, like horse, where the simplification is a skeletal outline of the original. 2) phonetic substitution such as the character 达. The original has a much more complicated character inside that is also pronounced "da", and is acting as the phonetic. This character just swapped out the phonetic for a simpler one. 3) Arbitrary substitution. This is just kind of the "ah screw it" attitude, like the character 体. The traditional character, 體, is a nice pictophonetic, with 骨, skeleton, indicating the meaning and 豊 (li) acting as a partial phonetic. It's simplified character is completely meaningless in both sound and meaning but it's a heck of a lot easier to write.
This is just an introduction to character etymology, but I really think learning the radicals and understanding the way they interact with each other can really help with memorization and also give you a deeper understanding toward meaning.
Good luck to you!
edit: Oh, it's an article link. That was dumb. Hope this was helpful to someone!