Now extract the contents of the package and upload the Scripts and Styles folder to any host or website which can be linked from your blog.
To make it work, you will need to edit your blog's template and add the following code after the <!-- end outer-wrapper --> tag:
<link href='http://[YOUR HOST URL]/SyntaxHighlighter.css' rel='stylesheet' type='text/css'/>
Now you just need to add support for the languages you want, I could just say, just put this bunch of code on your blog's template and it will work, but most people don't post code in several languages, also it's very important to understand what the hell you are doing.
To add syntax highlight support for python, after the shCore.js line you added before, add this line:
If you browse the Scripts folder of the syntaxhighlighter package, you will notice several shBrush*.js files, like shBrushPhp.js, these files are the highlight rules for especific languages, to support other languages, just change the shBrushPython in the above code to your language's specific file and add it to your template.
Syntaxhighlighter supports pre and textarea tags, but it will not work automagically, you need to specify that a pre or textarea tag is code and which language the code is.
To add some python code to your blog use:
<pre name="code" class="python">
The list of supported languages and their aliases can be found at the syntaxhighlighter wiki