First on the list is the File menu.
This should be a familiar sight, since nearly every software has a file menu where you can create, open, save and close files.
In Photoshop, you also have an option to save for Web and Devices. You might be hesitant to use it at first, but trust me, the name says it all.
Whenever you want to save an image for the web, use this option! It can help you to drastically reduce the image size while at the same time giving you a lot of settings to keep the quality of the image.