Video
We have several options here for changing the speed of the clip. The first drop-down menu lets you choose between constant and variable speed - leave it at constant for now. Below that you have two fields to enter values into - Duration and Speed. These two are linked, so that a change to one results in a change to the other. As you lower the speed, the duration gets longer, and as you increase the speed the duration gets shorter. You can either enter a new speed and let it choose the appropriate durations, or change the duration and let it choose the appropriate speed.
Lower speeds(<100%)/longer durations result in slow motion playback, while higher speeds(>100%)/shorter durations produce fast playback.
Just below the duration/Speed area you have a checkbox labeled Reverse which does just what it sounds like - it plays your video in reverse. The speed and duration controls still apply - this way you can have fast or slow motion combined with playback in reverse.
The second checkbox, labeled 'Frame Blending', is less self-explanatory, although it does exactly what it says it does - it blends frames together. When shooting on film, slow and fast motion is achieved by over- or under-cranking the camera - meaning you actually film more or fewer frames per second. When played back at normal projection speed the film is in slow or fast motion. Most video cameras, however, only record at a single frame rate. When you speed it up or slow it down in FCP you are just taking the same number of frames and playing them back at a different speed. This can result in motion which is not very smooth, especially when you slow your video down, because each frame is being held on screen for a longer period of time.
Frame blending helps to alleviate this problem by blending adjacent frames together to produce intermediate frames. While this can smooth out the motion of the video, it can also result in some blurriness, especially at very slow speeds. In general I recommend leaving it on, and if the playback quality isn't what you expect, try turning it off to see if it improves things.
If you are doing a significant amount of time manipulation in your videos it may be worth investing in Re:Vision Effects' Twixtor, which is a plug in for Final Cut and other video applications. It goes beyond FCP's simple frame blending to produce intermediate frames by tracking the movement of pixels between frames and then morphing the pixels to produce more accurate intermediates. It's not as good as actually shooting a higher frame rate with a film camera, but it's the next best thing, and produces significantly better results than Final Cut's built in speed tools.
You may need to drag the right side of your viewer window out in order to see the time remapping graph as shown above. This graph represents the progression through the frames in your clip over time. The vertical values are frames (0 - 440 in this case) while the horizontal axis is time. The diagonal green line represents a constant progression through the frames over time (constant speed). If your line is almost horizontal it may be because your clip is only a small suction of a much larger clip. Turning your clip into a subclip first will make the graph much easier to manage once you start manipulating the speed.
As you can see, all of the standard speed controls are available here and you can make constant speed changes just like you can from the speed window. However, the real power of this comes when you switch to variable speed. Change the drop-down menu at the top from "Constant Speed" to "Variable Speed" and the graph on the right will change as well, developing handles at each end and taking on an s-curve rather than a straight diagonal line. This causes your video to start out slowly, ramp up to slightly faster than full speed, and then slow to a stop on the last frame. You can manipulate the handles on each end of the curve to change the acceleration/deceleration of the clip.
To really start manipulating the time, switch the top menu back to constant speed (which resets the graph to a diagonal) and start adding keyframes to the graph using the pen tool (or option-clicking with the arrow tool). Once you move any of the keyframes from their initial positions the clip's playback speed will change to accommodate the new settings.
On the graph, constant 100% speed is represented by a diagonal line at the initial angle of the graph. Once you start adding keyframes the angle of the line changes and indicates the relative playback speed. A steeper line (than the original angle) indicates fast motion; a perfectly vertical line will just jump from one frame to the next instantly. A shallower angle indicates slow motion; a flat, horizontal line is actually a freeze frame. If the line angles down the video will actually play back in reverse. If you add curves to your graph (using the pen's smooth point tool) the curves indicate acceleration (curving up) or deceleration (curving down).
You can add as many keyframes to a clip as you like, and they can be changed to any value (frame) that you want, so you can achieve effects such as making the video rock back and forth between two points in time. The tricky part is to remember that each keyframes value affects the speed on either side of it. Since you have a certain number of frames to play back in a given time, slowing down one section requires you to speed up later in order to get to the last frame on time. If you want to slow down or speed up a section of a clip without changing the speed anywhere else in the clip you may need to change the final keyframe, which will cause the clip to end on a different frame.
The best way to learn how to use time remapping effectively is to experiment with it - if you ever get things so messed up that you can't make it do what you want, simply set the top menu back to constant speed to reset your graph.
There is more to time remapping than I've covered here, but this will get you started with the basics. To learn more about speed changes and time remapping check out chapter 16 in volume II of the Final Cut Pro User manual - it covers more aspects of monitoring how your speed is changing as well as using the time remapping tools (in the tool bar) to do time remapping in your timeline.