Using the Video Effects
You are going to begin to add the color effects the same way that you would with any video effect. Select the clip you want to alter in the Final Cut Pro Timeline and then go to your Browser. Select the Effects tab and then go to Video Effects. From here go down and start by selecting Image Control. Inside Final Cut Pro's Image Control you can find several options to shift the color tint of the overall image. The first you may want to try is Color Balance. This will allow you to control the degree of each color by increasing or decreasing Red, Greens, or Blues. This will shift the overall hue of the image in the direction you want.
One of the more simple options for changing the overall color of your video image is to use the Colorize video effect. Once this is dragged and dropped onto an image you will be able to Remap white and black in the direction of a selected color, which will dramatically change the color of the images in your project. You can also change the overall intensity of the color effect and this may want to be decreased unless you are trying to create a very dramatic effect. You will want to decrease the overall amount of the Colorize video effect for most situations.
Tint may be your default color effect in Final Cut Pro. Once this is applied to a clip you will essentially have two different options, one for the overall intensity of the Tint video effect and one for the color of the tint you are changing. Like with other color effects, you can also use the eye dropper to select a color to indicate.
Gradient Colorize is also going to be an option, but this is much more specific and if you want just an overall tint this may not be the choice to make. You will also have to set the Repat Method, the level of repeats, and the Map Channel.