1. Go to the repository, e.g.: https://bitbucket.org/username/repo_name/
2. On the left menu, choose branches
3. On the right side of the branches page, select Create branch
4. A popup window will appear, select Branch from and enter the new branch you want to create in the Branch name textbox
5. Click create

A new branch will be created

1. Go to the repository, e.g.:https://bitbucket.org/username/repo_name/
2. On the left menu, choose branches
3. Select the branch you want to delete from the branches page
4. Click on ... at the top right of the page, then click Delete branch
5. A confirmation popup will appear, click Confirm