I only know the ones I've seen in action, like Plan International, and they do very good work towards reducing dependency and helping people get the skills and knowledge that they need to pull themselves out of poverty and claim what's due to them.
I also have a lot of respect for Mujer y Salud, especially on the advocacy side of things.
There are others, like Intermón - especially their work on disaster preparedness/risk reduction, a couple of Italian agencies and their local partners in community-oriented eco-tourism initiatives in Salcedo and Samaná, and too many to mention - in the category of local organisations working in campos and barrios that I've come across over the 12+ years I've been involved in development work in this country. Of the religious ones, the Jesuits and CRS are worth mentioning.
Best way to help - depends what your interests/priorities are, but I recommend any of the ones named above.
I won't name the ones I think are little more than self-serving mechanisms to keep their executives and their friends and family in employment, but unfortunately there are a few national organisations and national branches of international organisations that fall into that category.
There are also several that may appear to "help" but really just prop up the status quo by maintaining people's helplessness and dependency - what is known in Spanish as asistencialismo.