Switches (also commonly called turnouts and points) are an essential part of any train layout. Whether it's a single switch to a small industrial siding, a major junction between two lines, or a busy yard ladder, switches make model railroad operations possible.
Railroads use a numbering system to classify the frog of the switch. The larger the number, the longer the frog. Modelers commonly use that same number to apply to the entire switch.
The number of a switch, or frog, is determined by the units of run required to create a divide of 1 unit. In model terms, these units are usually inches. So, if it takes six inches of length for the center lines of the two tracks to get one inch apart, you have a Number 6 switch. This does not mean a Number 6 switch is six inches long. That dimension refers to the track centerlines. Most Number 6 switches are about twice that length from end to end.
One common misconception about model switches is that a certain number corresponds to a particular radius of the track. Switch geometry doesn't work this way, and switches aren't a constant curve radius. There are exceptions to this; most commonly switches designed to take the place of a standard train set curve piece - 18" radius for example. These switches look very close in size to a No. 4 but are not the same. Most O-Gauge 3-Rail tracks are also marketed this way.
Unlike a typical "left" or "right" switch, wye switches have tracks that diverge in opposite directions simultaneously. Because of this, the numbering of a wye can be misleading. A Number 3 Wye switch sounds extremely tight, but it actually matches a Number 6 standard switch.
Wye switches get their name from their shape, and also from the track arrangement of the same name. A wye is used to turn locomotives or trains. It can be built without a wye switch, and wye switches can be used in other applications.
On curved switches, both tracks curve in the same direction, with the inner track obtaining a sharper radius. Some manufacturers do market them this way; other manufacturers use numbers, while others simply say "large radius, medium radius, etc."
All of this diversity can make things very difficult when planning a layout, even for experienced modelers. Some manufacturers offer templates online, and some track planning software packages are programmed with accurate templates. In other cases, you'll have to make your template from an actual switch.
Despite those efforts, often your only options are to buy what looks close and work around it, or build your switch, custom fit for your situation.
You can build your own switches by hand, or from kits. It is more work than simply tacking down a track piece, but the resulting look and operation of a switch that flows with the track is worth it. Like other skills, after you've done a few the work will go much faster. Given the higher cost and limited options in curved turnouts, this will likely remain the best option for some time.
In addition to switches where one track diverges into two, there are a number of special switches with multiple exit points. These are sometimes collectively called "puzzle switches." These can often be found in busy junctions or terminals.
A three-way switch is a switch with three diverging routes - essentially a left and a right switch combined. These can save a lot of space in compact switching areas on model railroads.
Slip switches and double-slip switches involve a pair of tracks which cross at a diamond. In addition to the crossing, trains can also travel from one route to the other in one or two directions. These are most commonly seen in large passenger terminals where multiple arrival tracks fan out into the station platforms.