Pines, firs and spruces trees are all conifers, or ever green trees with needle like leaves. According to stupidquestion.net the three terms evolved to discern between pines growing in different climates. Put succinctly: "a spruce is simply a fir from northeastern Europe, etymologically speaking. Likewise, a fir is just a cold-weather pine, and they're all pines in the end... Scientific classification won't tell you anything more than that-it'll just make you count needles to do it."
Of course, it's not always so simple, although it's true the best way to tell the difference is by looking at the leaves, or needles, as explained in detail at iastate.edu:
The needles on a "true pine" are attached to the branches in small clusters of two to five.
Spruce trees have needles attached individually to the branches, on small stalk like projections, which remain when the needles drop. The needles are sharply pointed, square and can be rolled between your fingers.
Firs, like spruces have needles attached individually to the branches, but with no projection. These needles are softer than Spruce, and are flat, so they do not roll between the fingers. When the needles drop, the branch has a smooth bark.
Thinking in terms of shape and suitability as Christmas trees, Spruce has the traditional Christmas tree shape, often with upturned branches. The branches have a bare underside, which can make hanging decorations easier, although the sharp needles can be awkward to work around. The Spruce also tends to drop it's needles more quickly than pines or firs. This can be mitigated by using an uncut tree and keeping it well watered.
Firs tend to have a bushy appearance, with tightly packed branches whose needles are spirally arranged, meaning they are great for giving a full effect. The length of the needles varies, but they are generally easier to hang decoration on, due to the softer needles, which last relatively well indoors.
Pines have a sparser, more open appearance with upturned branches that are quite widely spaced. This can mean a rather sorry looking Christmas tree unless lots of decorations are used. The pines do tend to hold their needles quite well, though.
To decide whether your tree is a pine, fir or spruce, first look at the branches. If the underside is bare, chances are it's a Spruce. To be sure, check the needles, which should be attached individually to the branch on raised nodules.
If there is no bare section on the branch, check the needles. If they are attached directly to the branch, it's a fir, if they are in clusters, it's a pine. So you don't really need to count the needles, just observe the way they are arranged on the branch, and a quick glance should be enough to distinguish between the three.