For most home users, the exploit would require you to visit a malicious Website where the attack could be carried out. The attack is also possible via compromised sites that may have malicious advertisements on them or host user-provided content. The most likely scenario for getting hit with this exploit appears to be phishing attempts where a hacker attempts to trick you into visiting a malicious site.
What Microsoft Advises
While Microsoft is working on a patch for the new IE exploit, the software maker is advising users to employ a multi-step workaround including downloading and installing a security toolkit, and setting your Internet security zone settings via Tools>Internet Options>Security to "High." The company is also advising you to configure Internet Explorer to either disable Active Scripting or prompt you before running any script. You can find out more details from Microsoft's security advisory.
Think About Switching, For Now
Employing this workaround will make it much harder to take advantage of the security threat, but it won't eliminate the problem entirely. That's a lot of hassle to go through just to mitigate but not eliminate a serious security flaw, which is why it might be more advisable to just dump IE until the problem is fixed.