How do I convert a shapefile to a raster image using ArcMap 10?
What functions within the conversion toolbox do I use?
I presume you have a point shapefile which you want to turn into raster.
There is an ArcMap 10 tool Point to Raster (Conversion) that should do the job.
You can set raster cell size and output raster image format, ie, .tif, .img etc.
More info can be found under the following link: http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//00120000002z000000
From within ArcMap you can manually save your map view to Tiff, Bmp, Pdf, etc. File, Export Map, Save as type.