The module r.in.gdal offers a common interface for many different raster formats. Try this first, especially since it also offers such practical options as on-the-fly location creation or extension of the default region in order to adapt it to the imported file.
If r.in.gdal does not suit your needs, use the appropriate r.in.* module (replace the * with the name of the format you wish to import).
After the import, you will probably want to run r.support in order to modify or create the GRASS support files.
For importing scanned maps, you will need to create a x,y-location according to the instructions in the chapter called Planning and constructing a GRASS database, scan the map in the desired resolution and save it into an appropriate raster format (e.g. tiff, jpeg, png, pbm) and then use r.in.gdal to import it. You will probably have to recify it in order to obtain geocoded data. the chapter called Processing Scanned Maps contains more information about this process.