I've heard of "soft lighting" and "hard lighting". What do these mean? How can I control how soft a light is?
The hardness or softness of a lightsource is determined entirely by the number of angles light is coming from (not the number of angles it's going to, that is the spread of the beam).
A lightsource producing light from many angles will have the effect of filling in shadows, and provide a gradual falloff (transition from lit to shadow). This is because as a surface curves away from the light the number of illumination angles slowly reduces. Contrast this with a hard source which produces light from only one angle. As a surface curves away from the light there becomes a point where the single lighting angle is at 90 degrees to the surface so the surface is no longer lit, giving a hard cutoff.
The biggest factor in the hardness or softness of a lightsource is the relative size of the light emitting surface. Large sources are in general soft* as they have a large illuminating surface, and thus each point will emit light from a different angle. You can make a lightsource bigger by putting a diffuse translucent object infront (this is called diffusing the light), the light shines out of a hard source from and single angle, and is then re-emmited from the diffusing material at many angles.
Here a relatively small lightsource results in a hard boundary between the lit and shaded side of the object.
Here a relatively large lightsource results in a softer transition from light to shade as the light can still reach the far side from certain angles.
I say relative size, as it's all to do with the angles. If you move a large source further away, the range of lighting angles decreases. The ultimate example of this is the sun. The sun has a huge light emitting surface, but is very far away, so there's little difference in angle of incidence between light coming from the top and bottom of the sun. The sun is thus a hard source, as demonstrated by the hard transition from light to shade you get on a sunny day.
*large sources can be hard, if they have something to limit the number of angles light is emmitted from, such as a grid or snoot.
Hard and soft lighting is actually a slight misnomer, as 'hard' and 'soft' actually refer more to the shadows cast by the lighting.
Hard lighting creates a shadow with a sharply defined 'hard' edge. Soft lighting gives a more gradual, soft edge to the shadow. A light can be so soft that it in fact casts very little discernible shadow at all.
To soften lighting, you need to diffuse it; in other words, you need to scatter it. Consider the sun. When there are no clouds and the Sun is bright, you can see well defined shadows everywhere: from the trees, from people, and even on people's faces where their features cast shadows. You can easily discern where the light source is from the direction of the shadows.
When the weather is cloudy, however, the clouds scatter the light across the sky, resulting in much softer light, and fewer, softer shadows: cloudy conditions are ideal for portraits, for this very reason.
In terms of artificial lighting, a hard light would be a clear glass bulb, or an on-camera flash. Softening artificial light depends on your equipment. If you have a speedlight with a swivel head, you can point it up at the ceiling or at a wall, so the light bounces off the surface and is scattered, or you can buy (or make) clip on diffusers. If you have true off-camera lighting, you can use a photographic umbrella or softbox to soften the light.