Check the lens too. Best way to check it but don't freak out...set the camera for f/11 and shoot a solid blue sky or white / cream colored wall then do an auto levels in Photoshop or post processing software. The dust will smack you in the head. Again, don't freak. Some go f/22 but I don't recommend shooting above f/11 anyway (except for macro work). If it's a bright day and I'm at an airshow, I use a ND or CPL Filter. F/11 and higher will introduce defraction on crop body cameras. That's where light to deflect off of the aperture blades making scattered light hit the sensor. .
Does your camera have a cleaning system? If so, leave it on. All my cams have them and they clean whenever I turn them on and then off. Keep the camera level when doing it.
Here's how Canon's works. Google yours. I forget the model you have.
http://cpn.canon-europe.com/content/education/technical/eos_integrated_cleaning_system.do
Regardless, you will likely have to wet-clean the sensor at some point. Although mine has been very good and clean for a few years now. I won't mess with either unless I see spots on my images.