There are two ways to approach this. Absorbing noise, or blocking it. I'll focus my comment on blocking, since just absorbing noise with wall panels and the like won't cut down the overal perceived sound level as much as just reduce reflections.
Blocking noise generally requires heavy, high mass materials (drywall, mass loaded vinyl sheeting, lead, concrete), specially damped wall panels (QuietRock), and/or isolation (decoupled walls, spring mounted ceiling tiles, RC clips, etc).
Single stud walls with double layer drywall works very well. Decoupled walls (staggered or double studs) with double layers of drywall does a better job. Use a visco-elastic glue (which acts as a dampening agent: GreenGlue or QuietGlue) between the 2 drywall layers and it'll work even better. Add MLV inside the wall, and you'll probably get a marginal increase in sound blockage, but may not be worth the extra cost. Place some acoustic absorbant foam on the noisy side of the barrier, and maybe it'll improve a bit more. Adding Homasote to the noisy side should also help.
A lot of this can be acheived with standard building materials, which should keep the cost down, but increase the overall size/weight/labor of the project.
If money isn't an object, then there are some easy to install but expensive materials:
Quietrock = ~$50 on up per 4x8 sheet (
http://www.quietsolution.com/html/quietrock.html)
Less expensive:
GreenGlue = ~$17 per 30oz tube for 1 4x8 panel (
http://www.greengluecompany.com/)
AND
Drywall = ~$9.50 per 4x8 sheet 1/2 inch (X2)
OR
Drywall AND
Homasote = ~$19 per 4x8 sheet 1/2 inch (probably not as efficient as QuietRock)
I hope this helps,
Steve