The type of minerals that form depend first on the basic chemical material that is available. For instance, it you have lots of iron and sulfur around, you would get different minerals than if you have mostly silicon and oxygen available.

Temperature and pressure also make a big difference in mineral formation. The basic chemical materials may be the same, but as the pressure and temperature change, the actual minerals will change too. Think of it like stacking wooden blocks -- you can stack the blocks so they have gaps between them or you can stack them so the blocks are extremely close together and touching. It is the same with minerals, the same basic chemical materials can be stacked in several different ways and you get several different minerals.

How tightly the mineral structure is packed depends on the temperature and pressure.Time will determine the size the crystals reach. If magma cools to rock slowly, the crystals will be larger. If the magma cools slowly, many tiny crystals will form.

Matter is stable in different states at different temperatures and pressures. Consider water, for example: at sea level, water is most stable in solid (ice) form below 0 C, and most stable in vapor form above 100 C, and can exist either as a vapor or as a liquid in-between. As you go up in the mountains, the pressure drops, and so does the boiling point, the point where liquid is no longer stable. Now, there are multiple phases of ice as well, different orientations of atoms within the crystal.

The same is true of all substances, although of course the numbers are different. Time, however, is required for the phase to change and for crystals to grow. Just getting water to the boiling point, as you know, does not cause it to all turn instantly into steam - it can take a while for it to boil away. Water tends to crystallize, melt, and otherwise change phase much more rapidly than many other substances - minerals take tremendous periods of time to change and grow. Diamond, for instance, is not stable at the surface of the Earth, but it takes eons for it to turn into graphite at surface pressure. If you heat it up, however, it will turn into graphite quite quickly.

Mineral formation, as you've already probably hypothesized, is a process involving the variables you've mentioned: heat, time and pressure. For minerals to form, they also need the raw materials that make up the finished mineral. All four of these are necessary to form minerals. The time that a mineral has to grow generally just determines its size. The longer it grows, the larger it will be.

Heat and pressure determine what type of mineral forms. Some minerals need very little heat and pressure to form (like quartz), and actually break up or melt if heated up or put under large amounts of pressure. Other types of minerals (metamorphic) need a lot of heat and pressure to form at low temperatures the mineral's raw materials can stay mixed up with other minerals' raw materials.

There are many types of minerals and places in the earth's crust where they can form. If you're interested you could look up hydrothermal deposits, magmatic minerals and metamorphic minerals to find out more.