This screencast shows you how to load vector and raster data into GRASS using the QGIS-GRASS plugin.

This screencast is ~ 9 minutes long and includes importing a shapefile and TIFF into a GRASS mapset.

The screencast is available at:
http://gisalaska.com/qgis_movies/qgis_grass_2.html

Errata:
Please note that I use the words layer and map interchangeably. Strictly speaking, in GRASS a mapset contains maps and a map contains one or more layers.

At one point the raster bands are referred to as mapsets - this is incorrect. They are individual layers within the raster map.