All the major web browsers have been patched for the vulnerability a while ago. So the way to avoid this attack is the same as avoiding any other piece of malware: just prevent malicious code from running on your machine. Viruses, worms, trojans, drive-bys, etc. - the delivery vector hasn't changed. Update your browser and OS, have an adblock extension blocking malware domains, don't download software from questionable sources, and you should be good to go. Use NoScript if you're extremely paranoid.
The most realistic attack scenario I can think of using this vulnerability is a nation-state attacking another nation-state or large corporation, trying to peer into virtual machines running on their servers. To pull that off would require extraordinary effort, patience, funding, expertise and mistakes on the part of the target (think Stuxnet). The average malware author looking to make a quick buck off of stealing random victims' bank accounts isn't going to be interested in using this.
