The first step is to study the coordinate plane pictured at left. There are many things to take note of. First of all, the plane (flat, 2D surface) is divided into four quadrants by way of two axes, one vertical and one horizontal. We call the horizontal axis the x-axis, and the vertical axis the y-axis. Notice how each axis has a positive and negative side, and are labeled as such. You will likely lose points if you forget to label your graph's axes on an exam.
The next thing to notice is the point where the two axes cross. We call this point the origin, and we say that its coordinates are (0, 0). This means that its "address" is 0 on the x-axis, and 0 on the y-axis. We must then scale the graph, which means determine the distance between each of the vertical and horizontal grid lines. In most cases, you will count by ones, as shown. However, it is important to understand that for some purposes, other values may be more practical. For example, you might see a graph in a new report where each line represents 10, or 100, or 1000. This might be the case if the graph dealt with time or money.
Notice how we have positive values on the right side of the x-axis, and negative values on the left side. We're really looking at a standard number line, with 0 in the middle. Notice how the y-axis is the same, but arranged vertically. The positive values are at the top, and the negative values are on the bottom.
Notice how the graph is divided into four quadrants. We use Roman numerals to name them, as shown above. Be sure to memorize which quadrant is which, as this is often tested.
We're now ready to name some points on the graph. Every point on the graph has an "address." Starting at the origin at the center, we first determine how far left or right we must go to be in line with the point, and then we determine how far up or down we have to go. Look at the purple square. To get to that point from the origin, we must move two units to the left (relative to the x-axis), and five units up (relative to the y-axis). We say that the coordinates of the purple square are (-2, 5).
The format of a coordinate is always (x, y), written like that in parentheses, separated by a comma. The x-coordinate is always listed before the y-coordinate. You can remember that they are in alphabetical order.
Look at the green star. Make sure you understand that its coordinates are (3, -2). The yellow rectangle is at (-4, -6), and the orange right triangle is at (1, 1). Sometimes the x and y-coordinates are the same. Don't be confused by that.
The most confusing plotted points for students are the ones that actually lie along one of the axes. Look at the red triangle. We must first determine how far left or right we have to go from the origin. We don't have to left or right at all! That means that the x-coordinate is 0. We now see that we must go 4 units up, which means the y-coordinate is 4. We can't just omit the x-coordinate. We have to write the coordinates of this point as (0, 4).
Look at the blue circle. Make sure you understand that its coordinates are (-5, 0). We must go 5 units to the left along the x-axis, and then we are already there! We don't have to go up or down at all, which means the y-value is 0.
Get some graph paper, and practice labeling and scaling your axes. Then practice plotting and identifying various points on the graph. This skill needs to become second-nature, otherwise you simply will not be able to progress to later work in math. The good news is that the system will never change. Once you learn how plotting points works, you'll always be able to plot or identify any point!