Here's my no-fail cradle cap removal method. First you have to buy a special shampoo at the store called T-Gel. This doesn't smell like baby shampoo, because it's NOT. The T stands for Tar. Pick up a fine tooth comb while you're there.
If you are intrigued rather than mortified at the idea of putting tar-in-shampoo-form on your baby's head, you're ready for the next step. Once you get home work some oil into the baby's scalp. Baby oil is of course the first choice, but I've used olive oil too. Massage it into the cradle cap and let it sit for a while. Better still if you do this in a steamy bathroom.
Strip down you and the baby and hop in the shower together (with the T-Gel and comb). When showering with the baby remember he is VERY slippery, especially once you start rinsing out the oil. When you change your grip on him make sure your other grip is already tight. It doesn't hurt to get dad in there too for an extra pair of hands. Tell him to MAINTAIN FOCUS.
I suppose my cradle cap removal plan could be done in a baby tub, but I think the shower steam is part of the magic. I also usually cradle the baby in my arms so his head is back and let the shower water do a really good rinse on his head, which is harder to do in a separate tub.
Now, put the T-Gel on his head, careful to keep it out of his eyes, and lather up. Next, use the comb to work under the layer of cradle cap. It should be flaking off really easily. Let the stubborn parts soak up some more tar while you work on easier parts. There should be gross little flakes all over. EW. Sometimes it's such a mess I have to rinse and re-apply the T-Gel.
This shouldn't hurt the baby, btw, just keep the shampoo out of his eyes. It's not runny and I've never had a problem with it. One cool thing with the water and T-Gel is it turns the cradle cap really white so you can see where it all is and go after it.
My little guy had a fully covered head of cradle cap and after one of my special treatments (it took 3 applications of T-Gel) I got rid of all of it and it didn't come back. Hope this helps!