The wheels are mildly polished aluminum with a clear coat finish. This is essentially the same urethane clear coat they use on the cars paint. Caring for it is about the same as the cars paint. First, do not use a dish washing detergent on automotive finishes. Detergents will strip any wax protection you might have on the car and it strips essential oils from the paint, basically drys it out. A proper automotive soap will be PH balanced and will not harm the paint. I'm personally a Meguiar's fan, but any should have these same attributes.
First, I'd try cleaning your wheels really well because if they're dirty this can considerably hinder their shine. After washing the cars paint I'd use the remaining wash soap with a soft cloth, or separate wash mitt (you don't want brake dust making it's way to your paint) to thoroughly clean the wheels and rinse. If they're really bad the next step is to use an automotive clay bar to remove bonded contaminants. Brake dust in particular can be bad. I use my pre-used clay bars from the paint to do wheels. After you do this the surface will be smooth as glass. When properly clean the stock wheels are fairly shiny.
If you want them shinier there are a couple of options. One is to take them to a professional polishing shop. They will use paint stripper to remove the clear coat then polish the aluminum to whatever level of gloss you want and then reapply clear coat. The only consideration with this is the center caps, which if I recall, are a faux aluminum under plastic so I doubt you would be able to get this to match the rest of the wheels if they were polished.
Of course the other option is chroming, which is an extremely durable finish with the ultimate shine. Either will be fairly expensive to have done though. I haven't seen an Insight with high polish or chrome wheels, but I did see a Prius a few weeks ago with its' wheels chromed and it looked good.
Griller is probably mixing up some commonly interchanged terms soap = detergent. There can be a big difference.
