You should be seeing Facebook as an option in the Share menu.

If Facebook is missing in the Share menu, click the "More" option. If you do not see Facebook at all.but have set up a Facebook account in the system preferences > Accounts, you may need to register the sharing extensions again.
See this fix:
If Mail is missing from that menu, restart your Mac, if you do not have done so.
If it remains missing, see this document: https://support.apple.com/en-us/HT203129
Follow these steps if the issue occured immediately after upgrading to Yosemite or El Capitan.
- Open the Terminal app, which is in the Utilities folder of your Applications folder.
- Type this command in Terminal:
/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/LaunchSe rvices.framework/Versions/A/Support/lsregister -kill -seed
- Press Return and wait for the Terminal prompt—which ends in $—to reappear. It may take a few minutes.
- Quit Terminal.
You should now see the expected Share
and Markup features. If not, go to Apple menu > System Preferences, click Extensions, and make sure that the Markup and sharing features are turned on in the Actions and Share Menu sections.
If another user account on your Mac has the same issue, log in to that account and repeat these steps.
The terminal command needs to go into a single line - with no line breaks and no space within LaunchServices.framework