I suppose that you have unique data for every marker on your map.
When you fetch markers data from internet or locally, you should save them into HashMap.
HashMap<Marker, String> map=new HashMap<Marker, String>();
for(MarkerInfo t : fetchedMarkerArray){
/* add your markers to map, and everything what you need*/
}
When you need to access to data you can easily do that by ( like Daan said you should implement OnMarkerClickListener):
onMarkerClick(Marker marker){
MarkerInfo m = (MarkerInfo)map.get(marker);
//show your fragment with data
}
If you have any additional questions, feel free to ask.