I'll part my hair and put the shampoo directly on my scalp - message it into my scalp, let it set for a moment, then rinse it out.
If your getting like a greasy / oily type of residue - that's actually what good shampoo is suppose to do. It's moisturizing your hair, and when you blow dry a lot of the residue will typically evaporate off, leaving just enough for a moist silky texture.
I have thick / dense hair and parting helps a lot with getting a good scrub on the scalp and making some room for excess residue to slide off in the rinsing process.
If anything - I'd try filling up a sink with water and sticking your head all the way in; the shampoo will float right off your scalp and into the water - then rinse with running water to get off the residue at the surface.
But if it's moisturizing residue - I recommend you keep that on your hair :) it seems to make my hair grow and develop healthier
I always make sure I put the shampoo on my scalp and massage it in. Conditioner I don't put on my scalp. I have one of those shower heads that you can take off, like at the hair salon, and it works pretty good.
It has nothing to do with how you put the shampoo on or how well you rinse it off. It is the shampoo itself... a lot of the generic brands leave what is called build-up in the hair making it look oily and well gross. What I would do is make the investment in a good brand of hair product one I suggest is Paul Mitchell tea tree moisturizing shampoo and conditioner, and then get one of the Paul Mitchell strengthening shampoo and conditioners. Switch back and forth from these two use the tea tree one week than the next week us the strengthening stuff. You will see a difference because not only are they a good brand... but you are shocking your hair week after week to keep that build up from happening! Good luck :)