How to crop images and reduce the size of a particular image using illustrator?

biochemadda,

If you mean what you may mean, namely to actually crop a raster image to a smaller pixel x pixel size with the help of Illy, you may create a rectangle with the desired size and position (remember to make it in whole pixel values), then select it along with the image and Object>Clipping Mask>Make.

This will merely make the outlying parts invisible, but then there is the dirty destructive deed, with the Clipping Mask selected:

1) In the Transparency palette/panel dropdown list select anything but Normal (Multiply is fine; this step may be unneeded in your version, you may try without it);

2) Object>Flatten Transparency, just keep the defaults including 100% Vector;

3) Shudder (optional, unless unavoidable).

This will crop thre image to the Bounding Box of the Clipping Path (the rectangle).

When you Export/Save for Web, the file size will reflect the new reduced size (depending on the settings).