Cycles Renders are noisy...

I’m a complete blender noob so please forgive me if this question is idiotic, but when I rendered my first model (a skyscraper) at 960x540 over 300 passes, the picture was very grainy and noisy. Here it is:

A link to the full size image

I’ve seen renders for which people claim to have used only 200 passes and they look incredibly sharp!

Is there anything I’m doing wrong or a setting which I should activate? Or is it simply a matter of computing power? My laptop is good for graphics, video and audio editing work, playing some decent games and doesn’t slow down during heavy usage despite being quite old. It has a Core 2 duo and an AMD Mobility Radeon GPU (1.7GB).

As a side note, can cycles actually make use of my GPU? I know it can make use of CUDA but I’m pretty sure that means it only works for certain Nvidia GPUs in SLI setups.

Any help would be… erm… helpful :o

A lot of Cycles images using a lot of glossy materials will need at least more than 1000 passes to clear up.

You can use the lightpath node to cheat on some shading to make things render faster while still making the final result look good due to some shading calculation and effects being omitted. One example would be to something like this, the camera see a glossy material, but the light only sees a diffuse material.