When solving a noise problem, you need to establish a few things:
1) Is the noise coming from within this space or is it coming from an adjacent space?
2) How loud is the noise in dBa (Decibels) Radio Shack sells a sound level meter for about $60, its not a very good one but it will put you in the ball park.
3) How loud would you like it to be. Keep in mind that most homes and office spaces are at or about 35 to 45 dBa to begin with. Dead Silence is not a reasonable goal.
Now for some answers:
If your noise source is in another room and you'd like to keep it there, you need to increase the transmission loss (TL) of the materials that make up the partitions between the rooms (i.e.,drywall, plaster, doors, windows). Products that increase the TL of a partition are rated with an STC (sound transmission class). Be very careful when looking for "Sound Proofing" products that do not give you an STC rating if you want them for increasing your TL. Some products will be rated with an NRC rating. The NRC rating is something completely different and is part of the most commonly misunderstood functions of acoustics. Sound Proof Foams are also usually a misrepresentation. In order to increase the TL of a partition, you must increase it's mass. Closed cell foam and spray on material don't do this. That's not to say that they don't have their place in acoustics. They just don't work for this problem. Look for products that have an STC rating of STC 26 or higher. Some of these may be a loaded vinyl barrier that weighs 1 or 2 pounds per square foot. Another great material is good old fashioned drywall. Adding an extra layer of drywall to an existing wall (as long as there are no holes in it) can make a dramatic improvement. You can kick it up a notch by mounting the drywall on isolation clips (try to stay away from resilient channel, it's to easy to short circuit).
Another thing to remember when buying soundproofing materials on the Internet is that you're dealing with a company that could be anywhere. Make certain that their website shows you who they are, where they are, and how to contact them via other means than e-mail. You should be able to call and speak to someone if you have questions. Soundproofing Stuff isn't cheap - don't be afraid to get help.