Edit: Updated Sept 1, 2014 to match WXF notation.
When learning Xiangqi, it is often quite useful to be able to notate games. In addition to being able to take notes and analyze past games, there are many books of annotated games. Most of these books are written in Chinese, but there are some online resources in English, such as XQ in English.
Games are most commonly notated in Chinese, but I will introduce a variant more easily used by Western players here.
A move in Xiangqi notation is expressed in 4 characters. The first two identify the piece to be moved, and the second two specify where the piece moves.
Identifying the right piece
In most cases, the piece is identified by its type (for example: pawn, elephant, cannon), and its file, the vertical line that its sitting on.
Each piece's type can be represented with a single letter. There are a couple slightly different systems in use, but I will be using the following:
Files are numbered from 1 to 9, right to left, from the perspective of the given player. For example, the chariot (俥) in the diagram below is "r7", since it is on the 7th file counting from the right, from red's perspective. The elephant, on the other hand is "e3", since it is on the 3rd file from the right, from black's perspective.
Occasionally, there will be two pieces of the same type on the same file, like the two cannons in the above diagram. In these cases, the piece further from the player is denoted "c+", and the piece closer to the player is "c-" for "back cannon". So the highlighted cannon on the board is "c+", since it is further from the black player's perspective, and the unhighlighted black cannon is "c-". Conversely, the highlighted horse is "h+", since it is further from red's perspective, and the unhighlighted horse is "h-".
Moving the piece
Where to move a piece is specified by the third and fourth characters in each move's notation. The third character specifies the direction in which the piece moves, and the fourth character specifies its destination. Xiangqi pieces can be categorized into those that move orthogonally (either horizontally or vertically), and those that don't. We'll go through the orthogonal movers first.
Pawns, cannons, chariots and generals move orthogonally. When the direction for an orthogonally moving piece is + or -, the piece moves forward or backward (according to the player's perspective) n number of steps, where n is the destination. When the direction for an orthogonally moving piece is ., the destination number specifies the file the piece is to end up on. Step through the following diagram for a couple examples.
Pieces such as the horse, elephant and adviser do not move orthogonally, and therefore never have a move specified with .; all their moves are + or -. For these pieces, the destination is always the file the piece ends up on. Step through the following diagram for a couple examples of non-orthogonal pieces.