Seems like now about every 6 months or so every asks this same question about some new vulnerability. The answer should be the same, do the same thing you should have been doing before this vulnerability came out.
In an Assumed Breach model of security, these vulnerability would have already existed, and your other network controls, in most cases, would have rendered them no worse than a phishing email (which has a much higher probability of impacting your organization).
A number of folks have said what needs to be said already about how to proceed with these specific vulnerabilities without all the hype, so I am just going to reference them and my own posts on Assume Breach:
Jake Williams with Rendition Infosec – Action Plan: https://www.renditioninfosec.com/2018/01/meltdown-and-sceptre-enterprise-action-plan/
Jake Williams with Rendition Infosec – Semi-technical explanation: https://www.renditioninfosec.com/2018/01/meltdown-and-spectre-vulnerability-slides/
Daniel Miessler – Simple Explanation: https://danielmiessler.com/blog/simple-explanation-difference-meltdown-spectre/
If any other posts are worth referencing that maybe I haven’t seen, I’ll gladly mention them here.