There is video tutorial on just this topic and a series of video
tutorials on web (i.e. bit-map) graphics.
On Page Setup pick Web Publish, then you can check the Paper popup
menu to see if there is a standard button or banner size that will
work for you, or set a custom size.
Page Setup is the main place, you want to learn about Fine Scale for
the palette click the m, i, p button over to p - for points. Set the
page size in Points (that is 72 per inch). Then if you export at 72
dpi, one point will be one pixel.
On Export pick Full Drawing Area, that will turn off anti-aliasing at
the border of the graphic. If you are exporting at 72 dpi,
measurements and page size will correspond to one "dot" - or Pixel.
If you adjust DPI, away from 72, there will then be more pixels in the
output. For example 144 DPI would double the size of the image.
And - it is not a good idea to just have "one" design for several
bitmap export sizes (especially something as important as a logo).
One design can cover a span of maybe 2 or so and still look
professional. But for decent looking graphics, you want to design
right to the size needed, for example a "Home" folder icon at 512x512
will have a lot of detail even window pains in house's windows. but
at 32 x 32 you will have totally different design with probably no
windows and just one rectangle for a front door. If you just "scale
down" the 512 design it will just be a blob.
Morph can be used to help with the different sizes. Or if the graphic
is simple - you can use Morph and resize that way. You can also
Export Just Graphics, then Morph - Export will do exactly what you
suggest.