A mast, a yard, and a square sail.
As opposed to the fore-and-aft sail, the square sail always takes the wind from the same side of the sail. The square sail is at its best when sailing before the wind, and is not good when beating against the wind, as shown on the figure below.
The arrows show the direction of the wind, and the left figure shows the path of a square rigger; the angle between the wind and the course you're able to keep is about 70 degrees. The right picture shows the path of a vessel with fore-and-aft sails; the angle here is only 40 degrees.
The square sail was mainly used on deep-water sailers, because it is a very effective and safe sail when sailing before the wind, and on long voyages you would always choose a route with as little tacking as possible.
Different kinds of riggings
Sailing ships are rated based on how they are rigged, and the most important aspect is where they are rigged with square sails and where they carry fore-and-aft sails. The following are the most important square rigged ship types:- The full-rigged ship or simply the ship has three or more masts and carries square sails on all of them.
- The barque has three or more masts and carries square sails on all but the aftermast, which is fore-and-aft rigged.
- The barquentine has three or more masts and carries square sails only on the foremast, and fore-and-aft sails on the rest.
- The brig is a two-masted vessel with both masts square rigged.
Masts
The tallest mast of the vessel is called the main mast. The mast before the main mast (if any) is called the fore mast. The masts after the main mast (if any) are called mizzen mast, jigger mast, driver mast and pusher mast; although the last two names have probably never been in common use. However, on five-masted barques and ships the masts are called fore mast, main mast, middle mast, mizzen mast, jigger mast. On the only five-masted full-rigged ship that was ever built, the Preussen, the middle mast was sometimes called the Laeisz mast, after the ship's owner F. Laeisz.Also, in America the term spanker mast was commonly used in reference to the aftermast of schooners. According to a letter from Captain Crowley of the seven-masted schooner Thomas W. Lawson they called the seven masts fore-, main-, mizzen-, number 4, number 5, number 6, and spanker-.
A fully square rigged mast consists of three spars - the lower mast, the topmast, and the topgallant mast. The rig has at least three square sails: the course on the lower mast, the topsail on the topmast and the topgallant sail on the topgallant mast.
Often, the topsail would get so big that is divided into two separate sails to be easier to handle - the lower topsail and the upper topsail; on large vessels the topgallant sail is also split in two for the same reason. Most big square riggers also have a royal above the topgallant sail, rigged on the royal mast, that is usually not a separate spar but just a lengthened topgallant mast. The sails are discussed further later on, let us first have a look at the standing rigging that support the masts:
Naturally, not all vessels were rigged exactly as has here been described; big vessels often had more than two pairs of backstays to support the topmast, for instance. Some (very few) had separate royal masts, and at the end of the 19th century when the spars were being made of steel, it became common to build the lower mast and the topmast as just one spar, but stays, shrouds and backstays were still rigged up as if there had been separate spars, as described above.
On the topmast is the topsail, often divided into the lower topsail and the upper topsail. On the topgallant mast is the topgallant sail, on big vessels divided into two sails, like the topsail. Topsail and topgallant sail are often pronounced tops'l and to'gan's'l, respectively. Often there is a sail above the topgallant sail called the royal, and clipper ships of the mid-19th century often carried skysails above the royals. Some even had a moonsail or moonraker above their main skysail.
There might never have been sails above the moonsails, but there are nonetheless names for them: heaven poker, angel poker, and cloud disturber.
On the stays that support the masts (blue on the sketches above) you often set triangular staysails. These are named after the stay on which they are rigged, so the sail on the topmast stay is called the topmast staysail. Before the foremast there are often many staysails (they are essential for the balance of the vessel), and these are called jibs.
Below is the four-masted barque Pamir with all her sails set. These are the names of the sails:
If the topsail is divided into two sails - this is usually the case - the lower topsail yard is in a fixed position on the very top of the lower mast, and only the upper topsail yard is hoisted. Because of this the topsail yards form pairs when the sails are not set. The same thing goes for double topgallant sails; the lower topgallant yard is fixed on top of the topmast, and only the upper topgallant yard is hoisted along the topgallant mast.
The following lines are used to operate a yard:
Additionally, big sails can have leechlines, that are fastened on the leeches and are used to bring the leeches up to the yard, which makes furling the sail easier. Sometimes, a leechline and a buntline is combined into a bunt-leechline that runs from the leech down to the foot and then up to the yard like an ordinary buntline.
Furthermore, a common alternative arrangement is to have the clewlines bring the clews not to the ends of the yards, but to the middle.
When taking in a sail that has a fixed yard, you haul the clewlines and the buntlines while you ease the sheets (or tacks), and then furl the sail (belaying the sail on the yard and securing it with gaskets). If the yard is not fixed the sail is taken in by easing the halyard while hauling the clewlines (or downhauls) and the buntlines.
If this explanation seemed complicated and theoretical, hopefully the following example will help clear things up:
On the right picture all the sails are set. The upper topsail yard and the topgallant yard have been hoisted and are in their highest positions. Their topping lifts (still blue) are not in use now, but trimming the course topping lifts affects all the yards since they are connected by sails and sheets. When the sails are to be taken in, you haul the clewlines (red) and the buntlines (grey). In reality, the buntlines would not be visible from astern since they run on the foreside of the sails. On the course and the lower topsail the clewlines bring the clews to the ends of the yard, but on the topgallant sail they bring them to the middle. The upper topsail doesn't have clewlines, but downhauls (orange) that are used to pull down the upper topsail yard to the lower topsail yard. Note that the course also has leechlines.
This is the lower mast looked at from the port side. It is supported by a stay (blue), eight shrouds (red, only the four port shrouds are visible), and two backstays (orange, only the port backstay is visible). Across the shrouds are put ratlines (often pronounced ratlins) that together with the shrouds form a ``net'' that you can climb on when you go aloft. Note though it is not made clear on the picture that there is only one stay, that goes straight forward, but two backstays, that go to each side of the ship.
Now the topmast has been rigged up. It is rigged on the foreside of the lower mast, and at this joint there is a small platform called the top (grey). The topmast is supported by the topmast stay (blue) and topmast shrouds (red) that go from the top of the topmast down to the outer edge of the top. The short green shrouds are called futtock shrouds and go from the outer edge of the top inwards to the lower mast, where they are fastened at a ring called the futtock that goes around the mast. There are two pairs of topmast backstays (orange). One pair is fastened at the same place as the topmast stay, and the other pair is at the absolute top of the topmast.
Here the topgallant mast is also rigged. It is actually a topgallant/royal mast done as only one spar. There is an arrengement similar to the top, but smaller, called the crosstrees (grey). The lower blue stay is the topgallant stay and the upper one is the royal stay. There is one pair of topgallant backstays (lower orange), and one pair of royal backstays (upper orange). There are also two topgallant shrouds (red) on each side. Royal shrouds are not present, as they are usually deemed unnecessary.
Sails
A square sail is named after the mast on which it is rigged. The sail on a lower mast is called the course; thus the sail of the lower mast of the fore mast (the fore lower mast) is called the fore course, and the course of the main mast is called the main course. The mizzen course, however, has a special name, crossjack, pronounced and sometimes written cro'jack. 
To maximize the sail area, clipper ships often rigged booms to lengthen the yeards, and carried additional sails on both sides of the square sails. These are called studding sails or stunsails, but were not in common use in the 20th century. The clipper ship Golden State on the painting has five stunsails on her foremast.
Rigging
On a square rigged mast, the course yard stands in a fixed position just below the top. The topsail yard is, when the sail is not set, a bit above the top. When you set the sail, you hoist the yard along the topmast up to its highest position just below the crosstrees. Top topgallant yard is hoisted from its lowest position just above the crosstrees, along the topgallant mast, to its highest position just below the location where the topgallant standing rigging (stays, shrouds and backstays) is fastened. Above the topgallant standing rigging is the royal yard, that is hoisted along the royal mast, but as noted earlier, the topgallant mast and royal mast are usually done as only one spar.
A square sail has four `edges' and four `corners'; the vertical edges at the sides of the sail are called leeches. The upper edge, that is attached to the yard, is called the head and the lower edge is called the foot. The two lower corners are called clews. To operate the sails themselves, the following lines are used:
Generally, a sail is set by unfurling it, (removing the gaskets and letting the sail fall down from the yard), letting go the clewlines and the buntlines, sheeting the sail (to bring the clews down to the yards below) and hoisting the yard. Naturally, if the yard is fixed you don't hoist it, and when setting upper topsails and upper topgallant sails you must let go of the downhauls. 
The left image is a mast looked at from astern. It is rigged with four square sails: a course, double topsails and a single topgallant sail. The course yard and the lower topsail yard are fixed, and the others are in their lowest positions because the sails are not set. All the yards are secured with their topping lifts (blue) except for the lower topsail yard that doesn't have any because it's connected to the upper topsail yard by the sail and the sheets not visible on the picture.
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