Here is the approach I found most helpful and what I tell the junior residents. Start by reading every scan of yours, cold. So don't look at the read, don't talk to rads just read the scan. Top to bottom. Try to develop a systematic way of doing it look at lung bases, then look at diaphragm, look for air or fluid, liver, then spleen, etc. Do this and come up with a diagnosis, every time. Whether that's "normal scan" or some pathology, and expect you will be wrong, but it helps to stake something to it so it's important to try to make your dx. Then look at the read and see how wrong you were. Go back through and see the things they commented on. See how they described them. Then go down to rads and ask, politely, if the rads attending will go over a scan with you. You've seen it twice now and know the dx, so spend the time listening to the way he describes what he is looking for and what he sees.
Do this every scan. Eventually you will start to see that you are catching some of the things in the read then most of them. Then you will find you just look at the read to confirm. Then you will start asking the radiologist things like "so the report says normal but the small bowel looks a little funny to me on slices 50 and 51, what am I seeing?" Again, to start with this will just be you being wrong, but eventually you will start catching things they miss.
There are systems for looking through scans like they teach for cxr but it really just matters that you are looking through that whole scan. What it mostly is is pattern recognition so you are just developing your subconscioius model of what normal looks like. Eventually you just sort of get to the point where abnormal things kind of jump out at you.