I've heard that it is better to shoot in 4:3 and then crop down to 16:9. How can I go about doing that in Final Cut Pro?

There's no way it's better to crop a 4:3 than to shoot in 16:9. But if you want your 4:3 to be letterbox (black bars on the top and bottom) go to effects>video filters>matte>widescreen.
But if you want it animorphic (for widescreen TVs) you can put it into an animorphic sequence and make the size huge to crop out the top and bottom, but it will lower the quality.

(It's not cropping down, because animorphic widescreen is 853 pixels wide and 4:3 is 720 pixels wide, you must just want to put black bars on the top and bottom to fake it?)

Brandon, it depends what sort of camera you have.

If you have a camera with a 16:9 native chip then it's definitely better to shoot 16:9.

If you have a camera with a 4:3 native chip that offers a 16:9 setting (without the use of anamorphic lenses etc, it just squeezes down or chucks away the data in the non 16:9 framing area) it is indeed generally better to shoot in a 4:3 ratio and mask for 16:9 in post, because it gives you more flexibility in moving your shots up and down in post.

If you want letterbox masking you can apply a widescreen matte from the video filters under Matte.

I use a Sony Pd170. Not true 16x9. Thanks for the tips. I've heard that 4x3 is the way to go...then mask later.