Are there any feasible ways to establish an off-earth colony with todays techonology? And what looks promising for traveling between solar-systems?

Its called terraforming. Its not just a star trek term anymore. check out this page . its all about mars colonization theory. Hope that helps.
http://www.redcolony.com/

As far as a travelling though space in order to get to our destination quicker we are limited by current levels of technology. However, there are many ideas for future propulsion systems which could be developed. A brief outline of propulsion systems is given here :
http://www.shu.ac.uk/schools/sci/sol/cgi/a...wers/space1.htm

And to think, some idiot in my friend's politics class thought that technology was 'maxed out' and wasn't going any further

...eih...bakaaa....