Click on the effects tab, which is located in the browser menu. It will be next to the tab that contains the raw footage for your current project.
Scroll through the different types of effects and filters. There will be options such as Video Effects, Video Filters and Video Transitions. When you click on one, a new menu will drop down and give you more specific effect options.
Select the specific effect you want to use from the drop-down menu. All you have to do is grab the effect with your mouse and drag it to the specific shot you want it applied to.
Re-render the video on your timeline by clicking the "Sequence" option at the top of the Final Cut window and then selecting "Render All." This will allow you to view and alter the video on the timeline with the effect.