Once these exploits become public knowledge and before a patch that fixes the vulnerability is provided, how can I defend my system as a private user?
The answer is to take responsibility for your own security.
If you rely only on software vendors for your security your trust is arguably misplaced and you might be disappointed quite often.
You are in control of your system as an individual and it is therefore your responsibility to take the necessary measures to protect what is important to you. Most software vendors care very little for you cat picture collection.
It all comes down to knowing what is on your system, how you use it, how important it is to you and how you can minimize exposure. The reputation of a software vendor is a great guide to knowing how much trust you should place in a piece of their software.
Having said this, you should know that even if you do all of these things you can only ever make an effort to minimize exposure and will never be immune to 0-day as even the most trustworthy software can be vulnerable in some way, and when this day comes it is your queue to reevaluate your risk and adjust your behavior and mitigation accordingly.
Remember: "The only secure computer is one that's unplugged, locked in a safe, and buried 20 feet under the ground in a secret location... and I'm not even too sure about that one" - Dennis Huges, FBI.
Edit: I forgot to mention a very important and relevant concept that ties in with some of the points made before. In order to mitigate the potential effects of a 0-day vulnerability in any particular piece of software you can make sure that in your environment you adhere to the the principle of least privilege. By constraining the privileges of the software you inherently limit the privileges of the the exploit*.
*Assuming the exploit does not make use of a privilege escalation vulnerability.