People forget that stone is a natural product. Granite is, generally, much less porous than marble, and thus innately better for counters you don't want to stain. However, it does depend a great deal on the stone. There is some granite out there that is exceptionally porous and even pretty soft, as granite goes.

Amysarah is right, it should have been sealed by the contractor, but if you want to keep it impervious, you'll need to re-seal it every so often. This is easy to do yourself, but you need the right product!!!

I had white granite counters in Egypt and a lot of the Egyptian granite is pretty porous. I once spilled some purple dye on it and it stained pretty well, but over time the stain faded and eventually just disappeared.

I currently have an island/table I did out of a stainless commercial frame with a slab of honed white marble on top. I liked the idea of a surface that develops patina, and so I really don't worry about it being sealed or panicking if I spill lemon juice on it. I think its beautiful and somehow truer to the material than pretending it's plastic.

There's another lesson here, too, which is to test "fixes" of any kind on a very small patch in a place that won't be noticed . . . sort of like when you get some salad dressing or other really messy food on your clothing, or someone dribbles some of that lovely dip finished so nicely with olive oil on your fabric-covered furniture, you test the spot-removed on an inside hem or on a place under the cushions. . . . . Who knows . . . .maybe the effects of the fix will only be temporary, but in any event, I'm totally with the others who have recommended that you call a pro, post-haste. ;o)

http://www.thisoldhouse.com/toh/how-to/intro/0,,20055946,00.html
Not exactly some randomly-googled untested old-wives-tale of an answer, so I don't blame you for trying it out.
Is is really awful? Is it in a spot that you could cover with a cutting board or a small appliance for a while? Ignore it until you've saved up some cash to get it fixed by a professional and get the whole shebang sealed at the same time.

I've done lots of granite kitchen counters (am an architect) - it's generally a better choice than marble precisely because it's more stain/heat resistant. (Tho a slab of white marble is great for pastry.)

You don't mention the type of granite (the most common, Absolute Black, is actually the most impervious,) nor the finish - polished is more resistant than honed. Regardless, given all the spotting/rings, it sounds like it was never properly sealed - which should have been part of the install.

I'd get in touch with the contractor who did the install - he should be willing to deal with it. (If very recent, it may even still be under warranty.) I don't know if the damage can be corrected (at least without sanding/refinishing whole slab), but if it can - simply sealing it should not be too costly. If the contractor isn't helpful, I'd get in touch with a good stone fabricator for advice and a rec of a local professional to do the work.

Can't help with removing the existing stain, but the stuff I use on my counter tops is Granite Gold. No problems so far...

Stiop googleing. Talk to a professional before you make matters worse. I am guessing as did I that you spent a fair chunk of change to purchase and have installed. Surly a few hundred dollars to a professional would be worth protecting your investment

Nutcakes is exactly right. I had an interior design business for years, and I am all for do it yourself, but at this point you need a pro before things get any further damage. After the treatment you can maintain with their prescribed treatment yourself. Hope it turns out well.

Oh dear. All I know is that you should be using a cleaner designed for granite, and also have sealed it initially and yearly after that. I would suspect that this homemade treatment was not sound, keep googling, but you may need to contact an expert in the subject and hire in at this point. It may be possible for it to be repolished and sealed. I'm not an expert in the subject, but I am dealing with a bad issue, like you on a coffee table (I suppose that is more minor), and also trying to prevent such damage on an extensive and beautiful pinkish and tan installed counter.

Oh, wow! Never having had any experience with granite countertops, all I can suggest is maybe contacting the people who put them in, or some home improvement place like Lowe's, and asking them?