I need to soundproof a room to prevent traffic noise (not honks, but engines etc). How can I approach this?
Here's an out of the box idea. How about active noise cancellation? put a few decent quality full range speakers in the room and find some noise-cancellation software or circuitry that you can tie in with a couple of mics that you orient toward the worst of the sound, and tune the system to cancel out external noise.
If that doesn't sound appealing:
Here's an interesting article: http://www.soundonsound.com/sos/may08/articles/soundproofing.htm
The first answer suggests "alaska pack" wall construction, which would be great but maybe you can't go quite that far.
You might be able to fir the existing walls out and fill the gap with a dense material. Sand is actually a very good sound insulator because it is very dense, and because a lot of energy is absorbed by friction between the sand grains. You could build a false floor the same way.
Do bear in mind that the sand will be very heavy. You should calculate the weight and maybe get an engineer involved in doing a bit of math to make sure the existing structure can take it.
If you build the panels out with 3/4" plywood and secure everything well enough to the existing framing (or are your walls masonry?), you might be able to build it in stages, against the wall, seal all the joints extremely well with something like caulk or spray foam, and pour sand into it, do the next layer, fill that with sand, etc. Then put in an acoustic drop ceiling like the first answer suggests.
You could maybe use spray foam instead of sand to fill the gap, but it won't absorb sound as well because it is nowhere near as dense. In that vein, though, you could also try gluing solid foam panels to your existing walls.
Low frequency sound (trucks on the freeway) will be the toughest to block. Low enough frequency sound travels right though the earth itself, so good luck with that.
Electrical outlets could be a problem. You can't hide any electrical junctions, so you would need to use some kind of extension boxes to pull them out to the new wall surface.
With difficulty. If you really mean "soundproof", you're essentially talking about the equivalent of building a sound studio, so I'd suggest websearching for discussions of building a home studio to learn the tricks and techniques. Depending on exactly how much sound you need to block, at what frequencies, there are different techniques. Don't forget floor and ceiling as possible paths, especially for low frequencies.
Discussed some of this with a friend who was building a fairly serious studio. Walls with offset studs (drywall on each side attaches only to every other stud, never both to the same stud) so there isn't a direct mechanical path from outside to inside; that cuts down bass leakage. Fill those walls with sand (yes, that's a lot of weight, and a maintenance hassle should you ever have to do anything to those walls; this was in his basement) to cut down treble leakage. Install an acoustic ceiling, suspended from elastic fittings, to reduce noise coming from above. (Which required that he increase headroom, which required that he sister joists with iron C-beam so he could cut back the wood and gain a few inches.) I think he had some specific design for the floor as well, but I don't remember what the plan was there.
Even so, he was mostly planning on recording at hours when there was minimal traffic in the area, and (I believe) he was assuming he'd have to turn off his heating system while recording to keep its noise from coming through.
And he didn't have to worry about windows. Or the door, since the studio door would open to the control room which was similarly soundproofed and would provide some isolation.
If you're willing to settle for just reducing the noise, there are less expensive things you can do.