Lightroom doesn't have much in the way of editing tools when working with video files, but it does have the ability to trim the beginning or end of video clips. While you can't then join the clips as you can with more conventional video editing software, it can be useful if you're just trying to quick share a single clip.
There are some common situations where there's comes in handy. You can pull out a short snippet from a longer clip. Or it allows you to remove the messy part at the beginning and end where you're composing the shot or turning the camera off.
It's not difficult to do, and because it uses the same kind of interface that most video editing software uses it will be intuitive if you've ever used other video editing apps, but accessing the tool isn't necessarily self-evident unless you know where to look for it.
First, open your video clip in single-item mode in the Library mode. If you try to do in the Develop module you'll get an error message.
You'll see the playback bar at the bottom of the video with a play button and a playhead. At the far right of that you'll see the timecode and then two small icons. You want the one at far right--the settings cog wheel.
When you click on that, the playback console will expand a little, showing a thumbnail timeline of the video clip and a couple of extra frame advance buttons.
But the parts you want at on each end of the visual timeline. There are two small handles there.
What you want to do is drag the handles to set new start points and end points for the clip.
That's about all there is to it.
As with nearly everything in Lightroom, this is a non-destructive process, so it's not actually cutting the original file. To see its effects, you'll need to export the video file, making sure to select either DPX or H.264, both of which render a new version of the video. If you select the Original option, the resulting video will be, well, the original and won't be trimmed.