Optimizing my shifts?

I finally feel comfortable driving my new car and I just have a few questions about it. I always shift before 3000 RPM's. But in order to get better acceleration I should shift just before I redline correct? I was told that this is the best way to accelerate quicker and get optimal performance. I know it will make the gas mileage much worse...but Will this hurt my car if I only do it sometimes? I taught myself how to drive it and was never told any of these things so I've just aired on the side of caution until now...which is probably a good idea since I just got out of the break-in period. Can anyone give me any tips about shifting and faster acceleration? Thanks!