Are you looking for generalities or specific keystrokes? I'm sorry, your question is a little vague. If you are looking for specifics, then here it is:
Photoshop
1. Open the original image and immediately re-save under a new filename. This preserves the original image.
2. Go to Image > Resize, then fill in the blanks in the RESIZE box:
3. Reset to 72 DPI for Internet
4. Ensure "proportional" box is checked
5. Resize to 640x480 (pretty standard) or whatever size is appropriate.
6. Save as a JPEG at MAXIMUM quality from the pull-down menus on the SAVE box.
7. Re-save at slightly lower and lower quality levels (HIGH, MEDIUM, LOW) until you get to a quality level that appears unsatisfactory (grainy, loss of colors).
8. Then hit EDIT > UNDO over and over until you backup to the lowest quality JPEG with a satisfactory appearance.
9. This should give you the smallest file with an acceptable appearance.
10. If you screw-up, close all your files and start again at step 1. The key is save under a new filename in step 1 so that your original is preserved.