The Sony DSC-H3 is a superzoom camera with a permanently-attached lens. You can't really get new lenses for it in the same sense one might with an interchangeable-lens camera. There are some things sold as telephoto lenses for such cameras, but really they are "teleside converters" — secondary lenses which attach in front of the permanent lens. I don't have any specific purchase advice, but will note that such a lens is likely to add aberrations and reduce sharpness, particularly if it's cheap. You might get okay results, but you might actually do just as well by just cropping and enlarging.
If you're seriously interested in getting some new lenses for it for experimentation purposes, I highly suggest you start considering an interchangeable lens system — either a DSLR or one of the new mirrorless camera systems like Sony's NEX. This will have more sticker shock, but if you really want to experiment with photography, you're going to want something like that eventually anyway. Might as well start sooner rather than putting money in a different direction.