How can I compress a larger video to a smaller size file?

An easy and simple way you can do this is by using Finder. It might not be the best option, depending on what you need but try it out.

Control+Click on the file and select > Encode Selected Video Files

You can choose from 480p, 720p, 1080p, Audio Only, or Apple ProRes under the Settings drop down menu.

Then choose whether you want to Encode for higher quality or greater compatability.

When you have selected your settings the window will tell you the Format, Resolution, Date rate and what it compatible with. The 480p, 720p and 1080p will use H.264 compression which is highly compressed and probably what you want to choose to compress your file.

After you have selected your settings select the destionation and if you want to delete the source file and click continue.

Done. Easy and simple, done right in finder.

You can also use an Application called Handbrake which will give you more options. But using finder should work just fine too.