The COLOR PALETTE starts out on the right hand side of your work area by default. Like the other toolbars, you can detach it, float it, move it... BUT, I suggest you leave all the customizing alone for a while so you can better work with tutorials and help that are designed with the default setup in mind <grin>
The ACTIVE COLORS PANEL has some confusing terminology. The two colored boxes are termed foreground color and background color but bascially they show the active colors for different tools. The foreground or top color is what appears when using tools like the brush, spray can, line draw, etc. The background or bottom color is what is used for background items like the border effect.
Squiggle your mouse across the "Rainbow Box" ... (in your PSP program, not here)... it will change into the eyedropper tool. If you left click on a color, you will change the top or foreground color box. If you right click on a color, it changes the bottom or background box. You can also click on the eyedropper tool on the left hand toolbar (Tool Palette) and choose colors from your image with the same left and right mouse clicks. You can choose colors as well by clicking on the active color box and choosing a new color in the color selection dialog box that appears but more about that and palette editing another day.
One last tip here... look close and you will see a small bent two-headed arrow by the active color boxes, click on it and the color positions will reverse with the bottom background color now the top foreground color and vice versa. This is real handy when you are working in two colors with the brush tool for example, put one in each box and click back and forth as needed.