Steps:
1. Open the desired image in Photoshop.
2. Crop. Select the crop tool then enter in your desired crop size In the top left corner. For this case (an avatar for the TPT forum) the max dimensions allowed are 90px x 90px. Adjust your crop as needed, then hit enter or click the check mark button above the image.

3. Save the avatar using the save for web function in Photoshop. Click on File, Save for Web & Devices... (Alt+Shift+Ctrl+S).

You can play around with some of the settings if you would like, but I would suggest just using JPEG, quality of 100 and Convert to sRGB.

Click on save and select your desired location then click save again.

Note: In the bottom left corner of the save for web window, the estimated output file size will appear. You may need to lower your quality or change other settings to decrease the file size depending on the limitations of the forum.
4. Close the file and DO NOT SAVE over the original image file.
Note: Again, DO NOT SAVE over the original image file, unless you really want to do that.

