The first three are fairly self-explanatory. You can learn philosophy by reading websites like Fallible Ideas and books by authors like David Deutsch and Karl Popper.
It's not too hard to find material teaching philosophical skills. This site lists and explains some logical fallacies. But the main way to learn them is through discussions. When you make a mistake of this kind, other more experienced philosophers will point it out to you. As long as you're using philosophy in discussions, then you can just learn these things as they come up. By the way, the best discussions, especially for beginners, are written discussions. Using text gives you the chance to reread things carefully, gives you all the time you need to think about what you want to say, and gives you the opportunity to look over your ideas and edit them before you communicate them. In verbal discussions, it can be pretty hard to catch all the details of what someone is saying in real time, and also hard to compose your reply in real time.
When I was new to philosophy, I was a terrible writer, and it took me forever to compose ideas. What did I do? I didn't take a course on writing, or read a book on how to write better. And I didn't study composing ideas faster either. All I did was participate in philosophical discussions, think, and learn over time. Eventually I got much faster, and learned to write more clearly. There's no need to work on these skills outside the context of actually doing philosophy.
Cultivating a rational attitude is a bit trickier. Discussion helps, but the less rationally you're discussing, the less you'll learn from it. Text discussions are easier because they help keep strong emotions out of it. Discussions should also be impersonal to make it easier; use hypothetical scenarios. Inventing impersonal examples involves separating the irrelevant personal details from the main issues, which can help you to understand better, so that's an added benefit.
Examples of a rational attitude are valuable. When you read a Karl Popper book, you can see how he makes a strong effort to look for ways his ideas might be mistaken. He also tries to understand other philosophers and consider charitable readings of their views, and tries not to let his emotions or biases cloud his judgment, and does other things like that. Maybe the best thing is to find someone who's better at it than you, and talk with him, and try to let him guide the discussion more than you do, and defer to his judgment a bit, so you can get a feel for what a more rational discussion is like and what it involves.
One happy fact is that you already have some skill in all of these areas. Everyone does because some philosophy is common knowledge in our culture. So you're not starting from scratch. All you really need to do is use what you already know to learn just a little bit more, and then do that again. Don't be discouraged if things start slow; the better at it you get, the faster you can improve.