You are developing your own application?
What do you consider to be an “osm map” ?. Do you mean tiles like http://tile.openstreetmap.org/mapnik/10/663/314.png ? If so then you have to download all the tiles of a city on your phone first. And do you want to zoom ? Then you have to download all tiles from different zoomlevels too.
That looks a pretty technical question to me. Such a tile is just a .png image. So you are asking how to show images (next to each other) in an android app ? Then this is not the right forum.