To get up to speed fast, I would use thader2012's advice above and literally work through the Beginner's Guide, User's Guide, and the other documentation linked above, building any sample programs described, and exploring what you can do beyond that when you have your own ideas to change the sample code the way you want it. Next, there is a link to Documentation in the site's main toolbar above. Choose any of the links in there that look interesting or relevant to stuff you want to build, and give it a try. Also, there are many websites and videos available online that offer free android programming tutorials. Assuming you are going to be working exclusively in Basic4Android, I recommend this step only for the general information you will pick up by seeing the process of what goes into the design and workings of Android applications. The actual coding will be Java and XML, but it will still have the same principles you will use in your own apps. A couple YouTube channels I can recommend are MyBringBack and TheNewBoston.
Finally, the support here in the forums is really great. The best and fastest way to learn here is to just start with an idea, start coding and designing with the things you learn in the documentation, search the forums when you get stuck, and if you can't find the answer to something or can't figure out an issue you are having in your code, post a new thread with a descriptive question that includes your issue, your code, and any other relevant info. The response time on the forums is generally under 24 hours, and the folks here are excellent and helpful.
Best of luck to you,
Eric H