Disclaimer: My opinions are solely my own and not based on psychological science (at least as far as I know).
I've always thought that things like depression and anxiety have some genetic component (the mix of chemicals in your brain) and some environmental 'trigger' component. You may not be able to do much about the genetic component, but if you get rid of the environmental component you can go a long way towards getting better.
I also have anxiety disorder. A lot of happiness has to do with being financially secure, having a fulfilling job/career, having a good social circle, eating well, having a good mix of hobbies, and working out. I've noticed that in my life whenever I was lagging in one or more of these areas, the anxiety and depression started bubbling up again. But whenever I tried taking care of these issues, I was mostly happy.
If someone is depressed, I don't think it will do to just give them some medications or tell them to do yoga, as you say. But maybe giving them meaningful employment or an exercise regimen will make them happy. Of course, people who are depressed get 'stuck' in a cycle where they are unable to 'break out' and obtain these things.
Again, these are solely my own opinions. Some of them might be stupid, others obvious.
That's sometimes a very frustrating thing to read- the "get rid of environmental triggers" thing. Speaking solely for myself here, my triggers are either really, really difficult to do anything about (financial difficulties) or a bad idea to try and get rid of (my academics). Sometimes you're just stuck at a point in your life where you can't fix your triggers.
I think there must be more we can do than get rid of triggers, or add more meaningful things. Maybe not as effective, but mental illness is a complex thing. Complex things have weak points. Sometimes I wonder of we're ignoring the trees and just seeing the forest here. Mental self-help advice is so... formulaic.
For a site extremely focused on fixing bad thinking patterns, I've noticed a bizarre lack of discussion here. Considering the high correlation between intelligence and mental illness, you'd think it would be a bigger topic.
I personally suffer from Generalized Anxiety Disorder and a very tame panic disorder. Most of this is focused on financial and academic things, but I will also get panicky about social interaction, responsibilities, and things that happened in the past that seriously shouldn't bother me. I have an almost amusing response to anxiety that is basically my brain panicking and telling me to go hide under my desk.
I know lukeprog and Alicorn managed to fight off a good deal of their issues in this area and wrote up how, but I don't think enough has been done. They mostly dealt with depression. What about rational schizophrenics and phobics and bipolar people? It's difficult to find anxiety advice that goes beyond "do yoga while watching the sunrise!" Pop psych isn't very helpful. I think LessWrong could be. What's mental illness but a wrongness in the head?
Mental illness seems to be worse to intelligent people than your typical biases, honestly. Hiding under my desk is even less useful than, say, appealing to authority during an argument. At least the latter has the potential to be useful. I know it's limiting me, and starting cycles of avoidance, and so much more. And my mental illness isn't even that bad! Trying to be rational and successful when schizophrenic sounds like a Sisyphusian nightmare.
I'm not fighting my difficulties nearly well enough to feel qualified to author my own posts. Hearing from people who are managing is more likely to help. If nothing else, maybe a Rational Support Group would be a lot of fun.