Welcome to Android Central! Open the Facebook app, tap "Photo" in the "What's on Your Mind?" posting box. In your Camera Roll, look for a video to post. Select it, then tap Post. Go from there.
Alternatively, go to Gallery or Photos, select a video, tap the Share button, and select Facebook.
It may be that uploading videos isn't possible using the Facebook mobile browser interface. I tried it, and like you, couldn't locate videos to upload.