Rainwater catchment systems (RWCSs) consist, in essence, of a collection surface such as a roof that directs water through guttering and/or piping to a storage vessel.
The key challenges in RWCSs are to be sure they collect and store enough water for the users that rely on them, and that the water is kept as clean and uncontaminated as possible.
See this booklet – palau_catchmentmanual – for some good information on building a RWCS.
See this booklet – construction-of-a-water-tank-for-micronesia-1 – for specific information on a low-tech, inexpensive way to build a RWCS.
Another way to collect drinking water is through solar distillation. See this video for an interesting, inexpensive, innovative approach that youth in Majuro are pursuing.