I assume you're using the Pro version with the video export capability? First you need to overlay the video using the export functionality. There is an export button on top of the session summary screen. Press that and it gives you a dialog with few option. Select the lap you want to export and set export type as "Overlaid video". Notice it takes a fair bit of storage space and time to export the video.
Once the video is overlaid and generated it will give you option to share it. If you have YouTube app configured, you can select that and the video directly through it. Notice, in version prior v3.30 beta, you can find the generated file in /DCIM/RaceChrono (or from the external sdcard if you selected that), if you need to copy it to your PC or if you dismissed the sharing dialog. In version v3.30 beta and newer, you can find the generated file in /Android/data/com.racechrono.pro/files/export/
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Once the video is overlaid and generated it will give you option to share it. If you have YouTube app configured, you can select that and the video directly through it. Notice, in version prior v3.30 beta, you can find the generated file in /DCIM/RaceChrono (or from the external sdcard if you selected that), if you need to copy it to your PC or if you dismissed the sharing dialog. In version v3.30 beta and newer, you can find the generated file in /Android/data/com.racechrono.pro/files/export/