Basically you're doing it right, but with the unnecessary step of using auto first. When using Av or Tv the exposure will still be set automatically. You probably want to use one of these modes, depending on the shot. For instance, with landscapes you want maximum depth of field, so this means a small aperture. So set Av mode and f/16 (as an example). For an action shot you might want a fast shutter speed, so set Tv and the appropriate shutter speed. In either case the camera will figure the exposure.
When you do this, note the "opposite" setting. When set to Av, make sure that the shutter speed is sufficiently fast enough to elimate/reduce camera shake. (1.6 times your lens length.) When set to Tv, make sure the aperture settings gives you enough depth of field for the picture. If the "opposite" setting is insufficient then raise your ISO setting one notch (from 100 to 200, for example) and check again.
So take a shot and check the LCD for the histogram and "blinkies" which indicate blown highlights. Adjust Exposure Compensation (EC) to brighten or darken the exposure based on your view of the histogram and/or blinkies. Don't try to judge the exposure from the picture in the LCD, since the LCD is often not very accurate and the brightness setting of the LCD can throw you off.
If you're concerned about correct exposures - and you should be until you get some good experience - then bracket the exposures. Take a shot at what the camera automatically chooses, then another at -2/3 EC, and another at +2/3 EC. For landscapes you'll have time to do this.
But the best thing you can do NOW is to practice. Go out and take some pictures. Try different settings and take lots of pictures of the same subject. Check the pics when you get home and try to gain some insight into what the settings do.
