There are two ways you can do this. The first method is to download the 1985.SQC file for the 1985 Cold War Crisis Campaign or the REDHAMMER.SQC file for the Red Hammer Campaign.
The second method is to use a cheat leaked out by Codemasters. While playing any campaign mission, press your keyboard's left SHIFT key along with the minus sign key ("-") on your keyboard's numeric key pad, let go and just type the word "campaign" without the quotes (no text box will appear - that's OK) and press the ENTER key. The words "CAMPAIGN ACTIVATED" should now appear on the upper left screen corner. Escape from the mission and go back to the campaign book and you should see all the campaign missions listed and be able to select any of them to play.