Scour the Websites
There are a number of websites that specialize in last minute deals. Skyscanner.com is a great option and will give you daily updates on the price of your desired flight. Holiday Pirates is another site that is worth taking a look at. Others have suggested that following your desired airline on Facebook or Twitter can help you get cheap last minute flights. Websites can also offer plenty of last minute hotel deals as well if you need one of those as well.
Even if you have someone that you wish to travel with you both may get better deals if you are willing to travel alone. It is much more likely that an airline will have one open seat (that no one wants as many people travel in pairs or more) than two or three. So you may be on different flights and arrive at different times but it can be worth it to get a good deal.