I had taught DS to use a sippy cup since the 4th month, but he really could master it in the 6~7th months.
The sippy cup he uses (and loves) is valve-free, hard sprout, with handles, and transparent. At that time I hadn't bought a soft sprout one to avoid possible nipple confusion (well perhaps I was too worried).
When DS did not tip the bottom up, I raised it a bit for him, so that he knew what he should have done to get the water down. Now he uses it like a pro!
And yes, we always offer the sippy cup whenever with solids to avoid constipation. But he never drinks (needs) more than 0.5 ounce each time (he is still breastfed frequently so no problem) .