Hi Nya,
The basemaps are static and aren't directly editable or selectable. You can however zoom to an area of interest and then go to the Share ribbon and select Map Export, then choose a format.
If you want to export tiles there is a specific basemap sevice for this but it is for the world imagery:
http://www.arcgis.com/home/item.html?id=226d23f076da478bba4589e7eae95952
And this is the terms of use for exporting tiles from those services:
http://downloads2.esri.com/ArcGISOnline/docs/tou_summary.pdf
Hope that helps.