The Icoformat plugin allows Photoshop to save images in ICO format. Each size of image should be saved as a separate ICO file.
Icobundle can then be used to combine the multiple ICOs into a single file. The operation varies depending on the operating system. On Mac OS the ICOs can be simply dropped onto the application whereas in Windows it operates as a command-line tool (instructions).
If you don't have Photoshop you could use an online favicon creator to generate the sizes required and then combine them with Icobundle. This one seems easy to use: http://www.genfavicon.com/.