There are several things that can help:
1) Make sure your image resolution is set to 72 dpi (Image > Image size)
2) Use RGB mode for images, not CMYK (Image > Mode)
3) Check to make sure there are no layers in your image; if so, flatten the image (Window > Layers > Flatten Image)
4) Save the file as a JPEG. There are two ways to do this: the first way is through (File > Save as) and then you can select compression amounts from 0 to 12, where 0 is very lossy and a small file, and 12 is maximum quality but a larger file.
5) The better way to save a JPEG for the web is to use (File > Save for Web). This will bring up a menu with lots of choices. You can optimize your file for a particular size.
I tried saving a test file as a JPEG with the 12 maximum quality, and saving for web with a target file size of 400K. I ended up with a 704K JPEG and a 60K JPEG, with little or no apparent difference on-screen. One-tenth the size!
You'll have to experiment a bit with settings because there is no one "best" setting for every image. Good luck!