I had heard before of that first study the article talks about, the different in praising intelligence vs. effort. I look at it this way: I know my kids are smart, but being told that is not going to help them do or learn anything. Intelligence isn't going to get you anywhere without other abilities like perseverance, confidence, and a willingness to try. We use the word "try" at our house a lot, that is really importance to us. Try something out, now when you want to give up just try a little more.
As for praise, I tend to say things like "Are you proud of what you did?" "Look how careful you're being!" "I like how much detail you're putting in your pictures" "you are really thinking hard about this, aren't you?" "I knew you could do that, you're such a hard worker" things like that. The other day she did something that took a lot of courage, and she told me "I'm so proud of how brave I was!" I don't want my kids to always be looking for praise and validation externally, I am hoping to teach them that it can come from inside, too.
When my 4 yr old (who loves the whole princess thing) dances around, I don't comment about how pretty she looks, I'll say things like "Look how strong you are, your legs can do such big kicks and leaps!" Body image is such a big issue now, that I want to lay the groundwork before she even gets to the preteen/teen years! Focusing on what your body can do rather than how it looks is important, so I try to really balance those comments out. She's told how pretty she is a lot, so I want to make sure she understands that physically she's a lot more than that.
I'll also just make observational comments, like "you're building a tall tower," "you put together the whole train track," "you climbed to the top of the slide." That way what they are doing is being acknowledged, but not praised per se.