Besides possibly some scientific methods there is no way to measure IBU's. You can estimate them using brewing software and ensuring that you change the default settings to accomodate the AA level of your hops.
It's something that you TARGET by choosing your hops and hop schedule wisely, and then you taste the finished product and see if it's what you wanted. It'll be something you get a feel for, so you can better pick an IBU target, and get your brewing process down so you can hit your target well.
But as far as actually measuring IBU's, it's not something you can do at home. You can send beer off for laboratory testing, but it's completely cost-prohibitive for homebrewing.