Triptych's answer is great. I just want to help you get more moo out of mootools.
$('results').setStyle('border','1px solid #000');
$('results').set('html','foo');
// all together now
$('results').setStyle('border','1px solid #000').set('html','foo');
You don't want to use innerHTML anymore if you're grabbing elements with $ (or using any framework, really).
Functions return something when they are called. Most methods (functions) in mootools return the thing it alters (like $('results')), so you can chain another function onto it.
Your examples aren't chaining. They are simply selecting properties of your object, not calling methods.
Mootools documentation is fantastic. You're just not familiar with the language enough yet. Mootools is considered to have a steeper learning curve, so that might be part of the problem.
I was like you, new to both mootools and javascript generally. After trudging through for a while I figured mootools out, and, unknowingly, learned javascript at the same time. The docs were integral to that.