How can I create my own offline map?

If you are creating offline basemaps for Fulcrum, you will want to use the raster based (not vector based) MBTiles portable map package format. 

If you already have GIS data, load them into TileMill (a free map design studio), design your map from your data, and export to an MBTiles file. Another option is a program called MapTiler. This is a much more user friendly alternative, but is not as robust as TileMill.