In url you added https://developers.google.com/youtube/v3/docs/videos/insert there is a section called "Response". In there you can read that after insert you get VideoResource:
{
"id": string,
"kind": "youtube#video",
"etag": etag,
"snippet": {
... ( and more... )
Key "id" contains id to your video. Your video can be found here http://www.youtube.com/watch?v={VIDEO_ID}