Carrie - I use a
Kodak Z612... it's discontinued now, but I am sure they have an equivalent in their current line up.
It's a long zoom with some manual features. I bought it as a bridge between my point and shoot and my next move to a dSLR. At the time, I didn't feel ready to make the best use of a dSLR, so I wanted something that could point and shoot, but that I could tinker with on manual settings.
Anyway, this camera has really served me well. I would recommend it. I thing the pictures it takes are great.
BUT that being said, I would guess that the camera you have currently probably has very similar features. Something that might help is doing a bit how-to reading on basic photography. I started with some scrapbooking sites that gave how-to tips for composing a great shot, and then did a little more technical reading on the manual features once I had a good feel for framing a shot. I can say that my pictures have come a long way in the last few years!
In any case, have fun with it

And always keep your camera on hand! You never know when a great shot will come along.