I want to use LaTex to write equations faster and if it is possible to export the result as a png or jpg so that it can be used on a website.
Wikipedia (and its opensource wiki engine) uses LaTeX for that, maybe there are some resources available (at least in the code, as it is opensource).
Your question is very broad. You could start with Amazon's List of Latex Books.
Here is a small symbol reference for LaTeX. If you are looking for something more as a general introduction, you can look at "The Not So Short Introduction To LaTeX2e". If you use Inkscape, there is built in support for rendering LaTeX and there are also extensions that do the same. You can read some commentary about it here. There are also things like LaTeX to HTML converters; However, at the time I was looking at them, they were somewhat limited in what formulas they could display.
You might want to investigate the StackExchange site mathoverflow.net solution - you can read about here. It uses jsMath which supports a lot of LaTeX syntax.
Assuming you already know a little LateX and your primary goal is to get images, a good high-level tool is mathTeX; there are even public servers that will convert to images for you.
If you want to do everything yourself, all the tools use dvipng
at bottom.
I taught myself LaTeX using the wikibook. It's fairly comprehensive as an initial guide. I've since bought The LaTeX Companion, which is a more advanced guide to in depth typesetting in LaTeX
I like both MathBin.net and Roger's Online Equation Editor. The latter lets you control the quality of the output. See also this question.
I use http://www.artofproblemsolving.com/LaTeX/AoPS_L_TeXer.php when I need a quick equation for a web site.
There are packages that will automatically produce images from LaTeX source, but these are often either buggy or used incorrectly. Many people install them on their blogs, for example, and the images show up if you visit the blog directly but they don't show up if you view the page via a blog reader. I'm not saying these problems can't be fixed. They can, but it often takes a few tries.
I prefer just to make a gif and stick it in the page. It's low tech and reliable.
One more tip: it's a good idea to put the LaTeX source in the alt tag of the image. This helps people using screen readers. It helps you too if you need to modify the equation later.