If you're using windows check your screen resolution.
You also need to have a monitor which is capable of handling 1080p resolution. 1920x1080 would be what you're looking to set your monitor resolution to.
The connection depends on your monitor, and what kind of inputs it has. Also, if you're using a TV with a VGA connector you may be limited to a maximum resolution of 1366x768 or something similar to that. In the case that you are, you'll never really get a true 1080p resolution from what I've come to understand. If you use an HDMI you can push 1080p but it's still compressed into a 1366x768 (or whatever the max resolution is)
I know this holds true for xbox 360, and my "1080p" tv will produce a 1080p picture in a compressed size. I can tell the difference when I look at my pc monitor with similar games, like borderlands, and Call of Duty series.
Your card should be working if you've installed the card and drivers and you have your video connection from the back of the card to the monitor.