Take a look at our faq for help in writing good questions.
You should only ask practical,
answerable questions based on actual
problems that you face.
This is a rather open-ended question, very similar to the question on producing documents.
Where to start learning?
Take a look at the list of available online resources listed as an aswer to the LaTeX online resources question.
LaTeX wikibook has a very good balance between accessibility and usefulness.
When you encounter a specific need or a problem, feel free to ask a question here. Be sure to include a minimal working example. Find out more about minimal working examples. Also, be sure to try and find the solution yourself at LaTeX wikibook first. You will be surprised how well its content matches the usual needs.
You might not get the entire solution, but be pointed to reading documentation for some package that will be useful for your need. LaTeX packages are usually well documented and will most likely have some examples for usage included.
Remarks on your question
I would like to fine tune each aspect of the page, from the title, to the headings, footnotes, fonts and so on
Some large packages can help you customize everything you mentioned and more.
If you would prefer using smaller packages for specific tasks, here are some sample packages:
What things do I have to study in
order to be able to customize LaTeX
(say, write a custom class)?
Classes are not very different from your documents. You could write all of the code you want directly in documents instead of including a class. But to avoid repetition, a set of useful commands is usually extracted to a class.
So your class might be as simple as including a couple of your favourite packages.
For example do I have to learn TeX
However, classes are usually more complex than a couple of your favourite packages. In order to write more complicated (and useful) code, you will have to learn some low-level TeX commands/macros.
Should I move on some graphic package?
If you would like to create nice illustrations for your documents (that will enable you to have consistent typography throughout your document), TikZ package is the way to go. As anything else LaTeX-related, the learning curve is rather high. On the other hand, it has a fantastic manual. Check some examples of figures created with TikZ.