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There are two ways to deal with noise: You either absorb it or you isolate it. (or both)
Isolation is by far superior, but with higher complexity and/or cost. Basically, you have to have a "2 leaf" system. You currently have a single leaf: The sheetmetal body itself! In order to get a 2nd leaf, you would have to apply a soft layer of material, followed by another layer with much higher mass. Most people use a light foam, covered by a vinyl mass layer. This will drop noise SIGNIFICANTLY! But you have to have complete isolation between the two layers. A recording studio, for example, will have a full solid wall to studs, air space, then to another set of studs with a 2nd full solid wall. Usually fiberglass insulation on each set of the studs, too. I have this in my studio and it can be over 120db inside of live music, with nothing over a whisper on the outside of the building.
Absorption, through use of materials like fiberglass and foam, will take noise and transfer it to heat. This works pretty well in most cases, but usually only takes away high frequency noise. It's cheap and easy to apply. Just put some padding under your carpet! Very simple... but again, not nearly as effective as isolation.
There are products like sound dampeners (dynomat) that help... it basically reduces resonance of your metal and adds a bit off mass to the sheet metal. This can help, but can also get expensive and won't be nearly as effective as isolation.
Can't stress enough: isolation. It makes a HUGE difference (when done right, of course). Though, you can make a pretty quiet ride by doing all the above. Just expect the weight of your wallet to go down and the weight of your car to go up quite a bit more.
As noted above, mass makes the difference. The more mass you put on, the less sound gets through. In a 2-leaf system, the more mass each leaf has, the more effective it will be. But do note: 1 beefy leaf won't beat a basic 2-leaf system. But 2 beefy leafs will dominate all!
As for myself: I used minimal sound dampening (the 1/4 center-coverage method) and did a layer of double-bubble foil wrap insulation under the carpet and attached EVERYWHERE possible on the car (firewall is very well covered), then just standard carpet w/o any foam or anything like that. This isn't extremely "noiseproof" but for the cost and the weight, was effective enough for me.
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