1) If you have lots of clips and titles, and graphics, etc, or layered video...
Drag select the section of clip(s) you want to export (use blade if necessary to create a dividing point), right click somewhere on any of them and "Create Compound Clip" Then "Share" the compound clip only. Very simple. If you don't need the compound clip and need to conserve space, tag it with a keyword like Unwanted and you can collect all the things you need to move to the trash later in order to clean house.
2)If you have only a simple segment of video without other layered graphics, video, titles, etc,
Just use the range select tool to select your in and out point on the clip, then click the "Share" icon at the top right of the Timeline window and you'll see it says, "Share this selection" or something like that at the top. It will only render the selection.
I was an editor for half a decade and I was at first upset at how I could do nothing the way I was trained to do it before, that basic functionality seemed missing. But after taking a Lynda.com course "Switching from FCP7 to FCPX" I realized that it wasn't missing functionality, it simply rethought editing from the ground up, instead of building off of decades old thinking and workflow. I frankly couldn't believe how impossible it was to see that until I took the course. It has some deficiencies, but they simply put the old system and workflow to shame. If you embrace this, you'll find yourselves (like me) able to do SO much more, instead of becoming that old linear editor you used to make fun of (we all know people that get stuck in the past, don't be one). It's a better way to work with footage and it has really freed me up to simply tell stories while thinking less about technicalities... and I always loved technicalities 😟
~John