Lets get right to the meat of it. Rationality is about thinking right, which helps you to come to better conclusions. The fundamental thing that makes a rationalist is the ability to admit when they're wrong. If you don't admit your wrong, you can't figure out what is right.
You gotta give more than lip service to this ideal, though. Whenever you analyze your beliefs (and you should be doing that pretty frequently) you should ask yourself "What would convince you this belief is wrong?" If you can't think of a reason you'd abandon that belief, you may be need to consider looking into other options.
I know. That sounds really wierd, doesn't it?
In science, when a hypothosis is presented, the single most important thing is that there has to be a way of testing the hypothosis, and that means that you have to be able to disprove the hypothosis. Science isn't actually about "proving" one particular angle, it's about disproving things until only the facts remain.
The barrier of falsification is a very important one. It should be the first you check when looking over your own beliefs.
Try this yourself. Pick a belief you hold dear; political, religious, scientific, or simply an opinion. Then, treating the opinion as a scientific hypothosis, do what scientists do, and try to prove yourself wrong. If you like, post your results for discussion and analysis!
NOTE : I plan on trying to post one of these a week, going over some basic rationalist principles. I don't intend for there to be a particular order or progression to them; just little bits and pieces mixed with experiments to try with your own thinking. This one was a little short; others may be longer.
Do remember that the content of the group is open to anyone; if you'd like to post your own experiments or debunkings, post pictures related to science or rationality, or start a discussion, feel free!