Rationality by itself is too far from your life to benefit from directly. The most direct application would be learning Bayes' Theorem, which tells you how to update on new evidence. In fact, the very concept of 'updating' is very useful. Being more rational means understanding when to change your mind, why, and how. But, you get a lot from rationality when you apply it to particular fields, and then seeing what those fields yield:

• Applying rationality to the science of desire allows you to learn how to modify your desires, which is essentially modifying your very self. You can break your wants down, analyze what goals you are trying to fulfill, and come up with better ways to fulfill those goals. Purchase Fuzzies and Utilons Separately

• Applying rationality to the science of emotions allows you to understand emotion in others (how it controls others) and more importantly learning to notice these emotions in yourself, understand what they communicate to you, and how to deal with them. Most important application is detecting Ugh fields.

• Applying rationality to making decisions allows you to understand how to make the best decision, when do you need more information, and how much that information is worth to you. (Example: consider how much would saving 10 minutes on your trip to work be worth to you. Would that be enough to justify moving closer to work, perhaps to a more expensive place?)

• Applying rationality to biases allows you to understand various biases that almost everyone succumbs to, detect when they occur in your own life, and systematically correct them. (Example: over-confidence bias. It's well known in computer science field that when you need to estimate how long a program will take to write, you make your best guess and multiply it by 2. The fact is, you might need to do that kind of correction in a lot of other estimates that you make in your life.)

• Applying rationality to beliefs allows you to know when you actually understand something, rather that feeling like you do. You can make predictions, you know what evidence will falsify your believes, you know where your beliefs come from. This means you are never stuck in a dead-end, and your believes aren't floating in space.

• Applying rationality to arguments allows you to argue with better results. You'll find the truth faster. You know when you need to give examples. You understand the concept of inferential distance, you know when you need to unpack various concepts.

There is a lot lot lot more, this is just a little bit that I got from the Anki cards I made so far (based on information presented at the rationality minicamp). There is a lot more and you only have to look at all the posts this community has created to see the benefits of being rational.