Welcome to the forum! I see you have a white Insight, which is a pretty popular color among forum members. I think you'll find great participation and helpful info here. Many of us are chasing the same 'holy grail' of fuel economy. Skim through the threads for some tips already posted, and shout if you have specific questions.
First, don't trust that the tank of gas you got with the car was totally full. If you're tracking MPG on Fuelly, start after your first fill-up.
My Insight is my first hybrid. It took a couple tanks to get the hang of it, but you'll find the technique that works for you. Look through this forum. There are many threads about techniques to improve mpg. I find if I can stick in the blue area of the power band and keep speed reasonable, you should be able to exceed the EPA estimates without issue. Be aware that low temperatures and winter gas will kill gas mileage. You probably bought at the best time - temps are warming, and summer gas will be available soon.
If you set your trip A and B meters to reset at engine off and full tank respectively, you'll have an easier time tracking in real time. I keep my trip A meter in front of me and use way-points on the way to/from work to compare results during drives.
Good luck with your new ride, and welcome to the forum. I'm sorry to hear about your Civic's demise. I went from a '99 Civic to my Insight. I feel like I left the stone age.