So there is a standard way to do this, you can first tag your image with the URI of your private repository, follow the below syntax :
docker tag [OPTIONS] IMAGE[:TAG] [REGISTRYHOST/][USERNAME/]NAME[:TAG]
Then once you are done tagging the image you want to push, just use the docker push command, like how it's given below :
docker push NAME[:TAG]
If the above doesn't work out, try logging into dockerhub account first
docker login --username username
Then tag your image with the correct repository
docker tag my-image username/my-repo
And then finally push it
docker push username/my-repo
Also If you want to become more adept with docker you can check this Docker training course . You will be trained by industry professionals who have years of experience in docker. Or you can check out this Docker Tutorial to get to know more about how to use docker.