Glass cook tops can get real dirty. Drips easily turn into a black backed on mess, if you are not careful. The good news is that the top can be restored to its factory finish. It does not have to stay dirty.
The best way to go about cleaning a glass top is to use a glass top cleaner. Glass cook top cleaners are none abrasive cleaners made for the job. Brand names matter very little. All are applied and used the same way. Their chemical composition is probably similar as well. The point is that they all work reasonably well. Don't stress out about what cleaner to use.
Begin by applying a generous amount of cleaner to the cold cook top. Gloves are a good ideal if you have delicate hands. Use a paper towel to spread the cleaner everywhere you want to clean. Let it dissolve the stains on the cook top for a few few minutes.
Using a new paper towel star rubbing the cook top all over. You will notice that some stains come right out; others, it seems, are not affected at all. Continue rubbing in the areas where you are making good progress. Switch for a new towel whoever the one you are holding gets loaded with dissolved grease. As long as the towel holds mostly fresh cleaner keep using it.
After some while you will be down to a few stains that do not dissolve at all. Wipe off all the cleaner left on the surface. Apply fresh cleaner directly onto the stains and let it sit for a few minutes. After the break start rubbing again. You will notice that the same thing is happening again. Some parts are easy to remove, while others seem unaffected. Repeat the process until all stains are gone.
This is happening because the cleaner can only attack the outer most layer of the stain. Some stains are thick enough to require four or more applications of the product. This does not mean your cleaner is not working. It just means you are looking at a tough stain.
In a few cases you can speed up the process using a good top scraper or a one sided razor blade in a holder. The mechanical action these tools create will remove thick stains more easily. The blades, however, are useless to remove thin stains. They will simply ride over them. You have to revert to using the cleaner eventually.
The cleaner I use most often is Weiman Glass top cleaner. So far the cleaner has cleaned up everything I wanted it too. I had to do a lot of rubbing, but I think you can't go wrong with Weiman's. If you know a better product, let us know.