First of all, the best advice is to find out if the operating systems you use are being updated with patches to mitigate the exploits. Most systems are — including upcoming Safari and Chrome patches that will be issued by Apple and Google which could reduce the risk of the Spectre exploit.
Some government cybersecurity officials worry that the latest software patches aren’t enough, and that low-level firmware updates could be required.
It’s also smart to practice safe computing strategies throughout all of your work on electronic devices — including the standard advice on avoiding computer viruses. Anti-virus software are already being updated to look out for viruses that use Meltdown and Exploit (so update them when you can).
Additionally, refrain from saving any passwords in your browser or cache, and be cautious about the websites and services that you use.