Summarize:

On the rear of your Roomba there is a tray that fills with dirt and dust as it vacuums (also called the "bin"). Press the button on top of this tray and remove it. Dump the contents of this tray into the trashcan. You should be able to see a red semi-circle inside the tray (which may be covered with gray dirt and dust). This is your filter. This filter will easily slide out of the tray, while remaining attached on one end. Slide this out, and knock any loose dirt/dust off into the trashcan. Attach the crevice tool (the long, thin attachment) to the hose of a regular vacuum cleaner. Then turn the vacuum on and use this attachment to remove dirt and grime from the Roomba collection tray and filter. Remove the crevice tool from your vacuum hose, and instead attach the brush tool. Turn your vacuum back on and go over the filter and tray once again. This time, pay extra attention to the surface of the filter, the rubber seals, and the vents on the back of the tray. When you are finished, snap the filter back into place.
Empty your Roomba. Remove the filter. Vacuum the tray and filter using a regular vacuum and the crevice tool. Switch to the brush tool.