Essentially, you have to learn the "feel" of the clutch takeup/engagement point. It does take time. My first manual transmission was in a '91 Nissan pickup. After a week or so of bucking and stalling, I finally began to feel through my foot and butt when the driveline was grabbing and would go at that point from slowly letting out the clutch pedal to fully releasing it. I got so good with the "feel" that on the steepest hill in town I could balance the truck using the gas and clutch so that I wouldn't roll back even a millimeter when the time came to go. And that truck didn't have a tach, so I had to do it by feel and what I could hear coming from the engine bay to determine revs. First gear is definitely the toughest to get right, after that its easy. And just in case anyone would criticize my technique, I traded that truck in at 160K miles (bought it at 40K miles, so 120K of it was all me) and it still had the original clutch and wasn't showing any signs of needing replacement anytime soon.
The Insight has always been to me an easy car to drive in terms of shifting. Like I think others have said, I usually give the car about 1,500 - 1,750 rpm, begin easing off the clutch pedal, and then as I feel the car getting underway I'm getting off the clutch completely. I don't know if its the clutch or throttle that seems to me to be touchier, but I've never managed to be able to do the same "balancing act" quite as nicely as I was in my old Nissan. Plus, since when I stop I usually want the car to go into Auto Stop, I'm into neutral and just quick to the gas on a hill when its time to go again. Actually that's probably the reason I can't balance my Insight as well as that old Nissan, I don't have to do it enough.
The only time I launch at anything over 1,750rpm would be when I autocross, usually I rev to about 2,500 - 3,000 rpm and dump the clutch as I hit the throttle full open to try and get the best start I can off the line. Don't know if it helps, but again, by feel, it seems to be the best to me as a compromise between lugging off the line and not wanting to completely burn out my clutch in one sitting.
And for point of comparison, my Insight now has over 78,000 miles and the clutch feels like it did when the car was young.