At the upper left click on Image
Move the mouse pointer down to Resize
Click on Image Size
A small window will pop up that will allow you to set the pixel width and height. If you want to use it as an avatar you need to set both the width and the height to 80. If your image is not square then 80 should be the largest side. Then click OK
Next click on File
Click on Save For Web
Another window will come up which will allow you to change file types and quality. Most likely you can just use the default settings for everything here. However, if the file size is still to large you can use this window to reduce the quality of the image with will also reduce the file size. Click on Ok
Then just name the file whatever you want and save it.
I hope that helps.
The version of Photo Shop I have is Elements 3. There are some differences in the versions so it may not be exactly the same on whatever version you're using. But you may be able to figure it out from this info.