Before you ‘share’ your final edit, make sure you’re using the best quality setting in Final Cut’s Playback Preference Pane, as follows:
Open your Final Cut project as usual
Go to Final Cut Pro > Preferences…
Go to the Playback tab, select ‘Use original or optimized media’ and choose ‘High Quality’ in the Playback Quality dropdown.
Close the window, and then Share (Export) your film to your computer in the usual way. Then go to YouTube and upload it.