One very good technique for making a fractal less noisy or grainy is to increase the rendering time (increase the quality setting in the render tab; for complex fractals I use at least 2000 quality, sometimes up to 5000). This will make the render sharper and cleaner looking.
Another very big factor involves what types of transforms you are using. Some fractals are inherently more crisp than others, and both examples I show above are of the "disk-spiral" type which is described in the second link. Diskspirals are very nice to work with, in my opinion, because they are relatively simple (generally only 3 or 4 transforms needed) and therefore relatively quick to render, and they usually result in exceptionally clean/crisp images.
Some things I would suggest, aside from trying out those tutorials (trust me, they help out a lot and will show you a lot of cool techniques), is to spend some time playing with only linear, sinusoidal, and spherical transforms. Make random batches of perhaps 25 fractals at a time with only those 3 types set to appear, and with only 2 or 3 transforms at a time, and look through the results until you find one that looks interesting. Then open the transform editor and start playing around with it, moving/expanding/rotating the triangles to get a feel for how it affects the fractal. Also look at the transform properties for each triangle and change the numbers around and get a feel for what each transform type does.
Note that you're not likely to end up with a lot of cool looking images by using only linear/sinusoidal/spherical, but this
will help you get much better control over how your fractals look. Then when you make more advanced fractals you will feel much more comfortable and your results will be even better.
