How to simply add a village or district name and location to OSM

Move the map to area of the village and zoom right in.If you click on edit and choose potlach 2, login,click options tick mouse Lat Long, then the mouse pointer will show its lat long match that to the co ordinates you saved for the village.To the left of the screen there are some icons using the scroll bar among "places" there is a village sign which you can drag to the correct coordinates.the box to the left allows you to name it and source it do that click away from the village click save fill in some details of what you have done and save again thats it. job done these may help http://wiki.openstreetmap.org/wiki/Video_tutorials

Two possibilities :
- you noted down the coordinates with POI's in your Iphone application. Find a way to export the POI's is GPX format then either upload them into one of the OSM editors (Portlatch2, JOSM, Merkaartor). Then simply add a new node tagged with "place" ("place=town" "village" or "hamlet" depending on the definition of the tag place in this country (I found this page here but not sure). The limits between the different 'place' values are country specific; check the wiki or contact the local mailing list to be sure about the criteria). More tags can be required like the place name, a reference, a postcode, etc...
- you don't have POI's but just a list of GPS coordinates (datum WGS84) : with JOSM editor, you have a simple feature which can help here, the "Add Node.." tool where you just type in the coordinates and the node is added at the right location. Then you just attach the related tags as described above and repeat the operation for the 10..15 locations you surveyed.

if you have an File at a common Format (GPX, Shape,KML) you can try to open that at Josm. But you should look over that data, that there isn't any duplicates.

Otherwise look at this page: http://wiki.openstreetmap.org/wiki/Import