How to make a transitional effect?

There are two effects available in Final Cut: Colorize and Threshold. They both do basically the same thing, however Colorize will be a little more subtle (generally a softer effect) and Threshold gives you extra parameters and so a little more control over the overall "hardness or softness" of the effect (you'll figure it out when you see it.)

To create the Fade In/Out of the effect, for both: keyframe the Intensity parameter from 0% to 100% (in) and back to 0% (out).

Colorize is in the Color category and Threshold is in Basics.

Move the playhead to the position/time you want the effect to begin. In the Effect Inspector, set the Intensity value to 0%. You should also see a small diamond shape show up on the right side. Click on it to set it (it will turn yellow orange).

Move the playhead to the position you want the effect to finish and simply change the value of Intensity (FCP will automatically add that keyframe for you.)

If you want the effect to stay on for some time... move the playhead to the position you want the effect to *begin* to fade out and click the Intensity keyframe diamond to manually set it this time. This will create a "hold" keyframe.

Then move the playhead you want the effect to end and simply drag the Intensity parameter to 0.

The simplest and quickest way is to split your clip, add the black and white effect to one half, add a cross dissolve and drag that cross dissolve to several seconds or whatever transitional period you want.