Once you had the right sippy/straw cup, how long did it take your DC to "get it" and start drinking out of it?
We have been trying to get A to drink out of a (Munchkin) sippy cup for the last couple months and she just recently got to the point where she would take a couple sips from it. I don't know if she figured it out or if it was a fluke, but more often than not she is usually just biting/chewing on it while the water/juice dribbles down her chin.
She doesn't refuse the sippy cup outright, she just doesn't drink out of it. Should I switch things up and try another brand? Is that going to confuse her and negate what little progress we have made? FWIW: We tried Munchkin straw cups and that was a huge FAIL. She did not get the sucking action at.all.

Re: how long to get used to sippy?
I did the straws and he got it pretty quickly.
To prep him for it, we would put the straw in the water and put a finger on top to trap the liquid in it and then would put it in his mouth and let a drop go in. Sorta like a rabbit/hamster water bottle.
after a bit of that then we didn't dribble it and he was would try to suck it. He started to suck the straw then we'd fill a bit more and then on to a really short straw (we cut it) in a little cup of water.
I want to say it took about a month of working on it from start to being good at the straw.
We never really used sippy cups. though now we will
We introduced the sippy ~7 months and he really started to understand the suck/tilt concept around 10 1/2 months. Until then, we had to prop it up for him. I may try another brand...we have just about every one under the sun in our cabinet! For a good couple months, he could only drink out of the Wee (HEB brand) ones. Now he can figure out pretty much all of them.
If you'd like to try introducing a straw cup, the way we got him to figure it out was with juice boxes. I'd lightly squeeze the sides of the box (enough so the juice would come up the straw) and he learned to suck on the straw that way. He had it down by the third time we tried a juice box. He still doesn't like straw cups as well as sippys, though, so we're just sticking with those for now.
My SIL kept telling me to wait for a while on the straw cups until S was older. They are a pretty big chocking hazard and it's very easy for little ones to aspirate the liquid into their lugs. She's a SLP, so she knows her stuff. Just a thought.
S still doesn't quite get the sippies with the hard plastic lids. We've had lots of luck with the Nuby ones, with the silicone (I think?) tops. Specifically, the Nuby Stages ones. They come with 3 nipples/tops for each cup. The first is like a bottle nipple, then a regular sippy top, then a straw-like top. The Nuby Stages ones are at WalMart, I've never been able to find them anywhere else.
sippy cup? never got used to it. EVER. my boys are dumb.
straw cup? first try. of course, I let them try with my big jug of water w/ a big ole straw. they loved that. and I did the whole "Look at mama, ok now do this (do sucking a straw motion)", since they're copycats, they just did it. maybe they're kinda smart?
anyway, they were about 10 months old, I guess.
I would not worry, she will get it.
With Abby she would absolutely flat out refuse (fit and all) any sippy until about 11 months. Well, she would let me give it to her with water in it, but did not know what to do with it (did not even try). But, if I put formula in it she would throw a huge fit. silly girl! We started trying around 7 months.
With J we started trying around 6-7 months but were not at all consistent with it. I would maybe remember once every 6 meals, bad mommy. I started getting pretty consistent with it about a month ago. It only took him a couple of tries before he got it, mostly because he wanted us to hold it for him and I wouldn't.
We started with the Munchkin silicone sippy but it drives me crazy since it is not spill proof. I just bought some playtex spill proof ones and plan on transitioning him to those soon.