To drag and drop filters onto clips first click on the effects tab of the browser window and then toggle open the bin labeled "Video Effects". This will show you a list of subcategories such as Blur and Distort in which the filters are grouped. Open the bin for the category you want, select a filter and drag it to a clip on the timeline, to the Viewer window (if you have the clip you want to apply the filter to open there), or the Canvas window (if the clip you want to apply the filter to is currently visible there). Once you drop the filter it will be applied to your clip.
You can apply as many filters as you want to a clip - each one will be added on top of any others which are already there, and the effects of all applied filters will be combined. The order in which you apply filters to a clip determines the order in which they are processed. This is important because it can significantly affects the end result of the filters.
For example, if you place a letterbox filter on a clip it will add black bars to the top and bottom to make your video look like it was shot in widescreen. If you then add a blur filter it will not only blur the video but also the edges of the letterbox effect, which is probably not what you want. Put the blur on first and the video will be blurry but the letterbox edges will still be sharp.
Sometimes you want to be able to preview an effect but don't want to wait for the entire clip to render. The keyboard shortcut Option-P will play your sequence displaying every frame. This means when there is an effect or transition that can't play in realtime playback will slow down to allow every frame to be displayed. This isn't useful for timing, but it lets you get a better idea of how the video will look without having to render it all. This also won't play audio because it can't be kept in sync with the video playback as it slows down. If you go back and preview the same clip again it will usually run faster the second time through because it caches the preview from the first time.
Another option for previewing a small segment of your clip is the Quickview window. From the menu bar select Tools>Quickview and a new window called the 'Tool Bench' will open with a tab called 'QuickView'. At the bottom of the window is a slider which lets you choose how long a preview you want - from 2 to 10 seconds. When you hit the play button (above the slider) it will preview every frame in the window from whatever point in the timeline your playhead is at. Once it hits the preview limit (set by the slider) it will loop, usually faster than the first time because it is playing the cached version of the video. If you have a lot of effects and the preview is running slowly you can drop the resolution using the drop-down menu in the upper left hand corner of the window. At half resolution it will take 1/4 the time to render the preview, and at quarter resolution it will take only 1/16 the time - of course the trade off is that your video will look very pixelated and you won't be able to see much detail.
Of course you can also change the filter settings in this tab. To see the results of your changes, make sure the sequence playhead is on the clip in the timeline so that it is visible on the Canvas; any changes you make in the filter tab will now be immediately updated in the Canvas window.
There are far too many different filters to cover all of them and their individual controls here - the best way to get a feel for what they all do is to try them out, change the controls and see how the effects change. You can also look in Volume III of the user manual for a listing of all filters or got to the Help Menu in FCP and choose 'Final Cut Pro HD Help" for a pdf version of the user manual. The effects are listed beginning on page 135 of volume 3.
From this point it works just like audio mixing. Use the pen tool (or hold option while using the arrow tool) to add points to the line. Drag the points up or down to change the value at that point in time. Hold the Apple key while you drag to change the value more slowly as you drag(for greater precision). Preview your clip to see how the filter changes over time. When you have that property set the way you want, control-click to select another property or filter to change and repeat the process until the effect changes the way you want it to.
This will get you started with using Filters - there's not a whole lot more to it than this, it's a fairly straightforward topic. However, we'll be going deeper into the keyframing process and looking at different ways to work with keyframes next week. For now, this basic method of working with them on the timeline will get you started.