With many lasers the beam is produced by very small area. This means, that diffraction disperse the beam into cone, even if the photons travel parallel inside the medium. For diode lasers its usually about 30 degrees wide, for green DPSS it's like 10 degrees or even less.
Collimated beam means the beam has lowest possible divergence, in ideal (unrealistic) case the beam would be column.
To get such beam, you need convex lens, and you have to place the laser into it's focal point. It's one of the basics of optics .. rays coming from focal point will be parallel after passing convex lens.
This is the simple stuff. Now the more complex.
Colors. Any lens will suffer from reflection and transmission losses. That's why the lens are usually coated. But such coating is usually good only for some wavelengths - ie. colors. Lens coated for 445nm will reflect a lot of red for example. Uncoated lens can mostly be used for any color, as long as the lens material passes the wavelength well. For example glass is good for visible wavelengths, but cannot be used for deep IR, like CO2 lasers.
Next aspect is lens size, shape and focal distance. As for size .. if you want good divergence, you need WIDE beam at aperture. Wide beam disperses slower then thin beam. That's why airborne laser in my avatar pic has 2m diameter mirror. That's why you need beam EXPANDER to improve divergence of laser pointers.
As for focal distance .. you want to have laser in the focal point .. and use as much lens surface as possible. So the focal distance should be such, that raw laser beam cone just covers the lens when the laser is placed in lens focal point. For diode lasers it means the focal distance should be about the same as lens diameter, for DPSS lasers it has to be more, for example 5 times the diameter.
As for shape, usual convex lens is not good, because of spherical aberration. For collimation alone, plani-convex lens is usually good enough, with flat face toward diode and curved face toward parallel beam. Often lens consisting on more elements are used, but with single color there is not much need for that.
Most of the time, getting custom optics, with desired shape, focal length and coating .. is expensive. Even 12mm diameter good glass coated lens, manufactures by thousands, can cost you $50. That's why most of the time, you use something available. And most of the time, lens assembly comes with module, to which you place the diode itself. So you don't need to design things like distance of lens to diode. You only have to design your heatsink so it fits the module.
. I appreciate it a lot.