A good FAQ on both can be found at meltdownattack.com/. It even includes video clips of several exploits of the vulnerabilities. However, while I feel the chance of your personal device(s) being exploited are small, computer-based sites and services you use COULD be affected if they are not proactive.
What makes these vulnerabilities different from the rest of the malware that technology users deal with on a regular basis, is they are not found in the operating system (Windows, MacOS, Android OS, Linux kernel, etc). They are in the hard-coded instruction sets of the physical processor in the device, so the only thing processor manufacturers can do is fix what they are making now. Therefore, it will be up to the software being run on current processors to protect us. Most operating system providers have and/or are developing patches aimed at preventing exploits of the vulnerabilities, but it will ultimately be up to system administrators to implement them.
Lastly, another thing that makes Meltdown and Spectre unusual is that they were brought to everyone's attention by researchers and to date there have been no documented malicious exploits.