The other answers address the details of the question (OP needed to change "channel" to stop getting Beta upgrades).
To answer the question in the title "How to get Firefox to stop asking me to upgrade?", I think the procedure is:
- Go to the Options menu and select "Options"
- Switch to the Advanced options, and then to the Update tab within Advanced options
- Select "Never check for updates (not recommended: security risk)"
- Press OK
A similar question is "How to get Firefox to stop asking me to upgrade so frequently?". For example, at the moment I don't want to upgrade to Firefox 15, so I keep choosing "Ask Later" when it asks me to.
I want it to stop asking every day (every 86,400 seconds), but I don't want to completely forget about it. To change it to every week (every 604,800 seconds):
- Type about:config in the URL bar and hit Enter
- Confirm the question that you will be careful
- Enter app.update.interval in the search field right below the address bar
- Set the value of app.update.interval to "604800"
The setting is remembered when you close the webpage