If you have Final Cut7, it should have come bundled with Apple Motion, which would be the preferred way to do this effect. ( If you have FCP-X, you are asking this in the wrong forum)
Assuming you don’t have Motion and need to do this in the FCP7 timeline, it’s all in the Final Cut Motion tab, and you do it using keyframes.

To get the hang of this, double-click a clip to highlight it. Go to the Motion tab. Where you see the control for “center”, click that, and a little plus sign shows up on your viewer; use this to drag the clip off to the right, then click the little diamond-marked button to make a keyframe. Play the clip to the end, stop there.
Again, use the “center” button and the little plus sign to drag the clip to the other side of the screen. Mark a keyframe. Play this back from the beginning, and the clip should travel across the screen. Use the scale control to shrink the clips if you need to.
Another thing to try is to check out the effects that came with the system: you may have a plug-in that already automates this process. If not, you will need to put clips on two video tracks, alternating, and keyframe each one independently.
Apple Motion really makes this kind of thing much easier. You sure you don’t have that app?