From a purely utilitarian standpoint, to help communities abroad in need, there is one gold standard: spend your time moonlighting, save the money, then write a check to donate to experts on the ground who can assist with training up local resources and running programs on the ground. But this obviously is not as sexy as actually doing the work hands-on directly. And I respect that.
If you are interested in actually providing quality care, you will be looking to do provide sustainable care locally. The sustainable adjective is what separates actual development work from tourism. The sustainable aspect also suggests doing less hands on care of locals in the community and more skills development of other professionals who will be there long after you leave. So to provide this care, your best bet is going to be become the best psychiatrist you can be and get plenty of experience working in resource-constrained environments (which is consistent with most county-funded training environments).
Many psychiatry residencies will highlight their "international psychiatry" credentials. Some are the "2 months in Haiti" or "1 month in Congo." Some of these are outright exploitive. Some of them are built on the efforts of a few faculty who have funding for international development efforts. For the latter category, resident participation is fine (and immensely satisfying; who doesn't want to treat the world's poor?) but the net outcome of the work is not the time spent by residents at the clinic but the dull-to-most work done at the higher levels allocating funds for medicine, physical plant, and training materials. That's where the good happens. Not the work done in the clinic for the month.
If you want to get involved in international psychiatry, look at residencies that have fellowships in global psychiatry. I'm not advocating that you should do one, but these programs that have fellowships (and/or masters or MPH in global health) tend to attract faculty who do research in the area and have funds to develop sustainable care in their target communities. Get involved heavily in the behind the scenes work that leads to the boots-on-ground care. You'll get a lot more out of one of these training settings than you will at most programs that offer the "1 month in Congo," which is typically one or two faculty members that did a month in Congo when they were residents and keep that train going. Outcome and benefits of such programs are highly variable.
And last point, if you want to really get involved in things like Doctors Without Borders and the like (MSF has a massive advertising budget, so they are the ones folks tend to think of first, though their psych is not the model), you already have one of the qualities they like to see, which is past experience living in a developing nation. If you are serious about doing good work, devote time in residency to learning Spanish or French (or another language if you have a specific region in mind). Work hard in residency developing excellent clinical chops, particularly with psychopharmacology (particularly generics). Get as much experience with teaching as you can (this will be the biggest bang you can have in a developing world context). Align yourself with folks who do research on outcomes in this area.
Doing the elective "2 months in Haiti" or "1 month in Congo" would be a heap of fun and you'll get great photographs, but I wouldn't opt for a school that has that over another program with better training that didn't. The developing world needs well-trained providers, not folks heading down as hobbyists.
