Here are the steps for how I do these tasks:
Adding a New Login:
The procedure below assumes that you have the website’s account registration form open in your browser, and that your Bitwarden browser extension is currently unlocked:
1.Open the browser extension (click Bitwarden 
icon at the top of the browser, or press Ctrl+Shift+Y).
2. Click 
(or the “Add a Login” link).
3. Type the desired username (or generate a random one).
4. Click the 
icon the in Password field (generate password).
5. Click Select in the upper right corner.
6. Click Save in the upper right corner.
7. You will now see the new vault item listed at the top of the browser extension’s “Tab” page → click on the website name (which will transfer your username and password to the website’s account registration form.
8. In your browser, submit the account registration form to the website server.
Changing a Password:
The procedure below assumes that you have the website’s password change form open in your browser, and that your Bitwarden browser extension is currently unlocked:
1.Open the browser extension (click Bitwarden icon at the top of the browser, or press Ctrl+Shift+Y).
2. Open the vault item in the browser extension (click the “View” icon).
3. Copy the old password to the clipboard.*
4. Click “Edit” in the upper right corner.
5. In the password field, click to go to the password generator.
6. Click “OK” at the warning prompt about overwriting the password.
7. Click “Select” in the upper right corner.
8. Click “Save” in the upper right corner.
9. Click the “Auto-fill” button (below the displayed item details).
10. On the website’s password change form, delete the contents of the “Old Password” field and paste in the old password from the clipboard.*
11. Submit the password change form to the website server.
*Depending on how quickly you can complete Steps 4–10 and what setting you have for the clipboard timeout option, you may find that the old password has been cleared from the clipboard by the time that you need to paste it. In this case, you can retrieve the old password from the Password History (which stores the 5 most recent passwords).
Unrelated Rant: Step 6 in the above password change procedure is an unnecessary annoyance, but it is a requirement that Bitwarden has implemented. If you agree that this extra confirmation step is superfluous and should be eliminated, please vote for the following feature request: