galled, I think it depends on what comes naturally to you. If I'm adding a bunch of two digit numbers, I first focus on the tens digits and try to put them in pairs that add to ten to figure out the approximate hundreds digit. I then add up the remaining tens digits. I tackle the units digits similarly. There are other nuances, but there are too many edge cases to explain in a concise manner.
Mental, 'fun', and quick computation takes a LOT of practice. In middle school, I had 2 hour mandatory practice sessions at least 2-3 times a week plus my own practice to stay competitive, and my own practice was just to keep up with my own school. I'm glad I stepped back in high school because the environment attracted a lot of really toxic people.