Spectre and Meltdown are two of the most ubiquitous bugs to have hit computers in recent memory because they affect just about every processor Intel and AMD have released over the past few years. If you're not sure whether your system is vulnerable to the bug though, you need to find out in order to get the patch you need to fix it. The best way to do that now, is to use the InSpectre checker tool from Steve Gibson.
The tool not only checks your system to see if it is vulnerable to the two flaws, but also recommends fixes for you if you are. It may be as simple as updating your operating system to run the latest version which shores up the holes, or it could be that it recommends you perform a motherboard chipset driver update. In some cases a BIOS flash might be in order, but that's in rarer cases.
It is worth pointing out though, that some of the fixes being touted by Microsoft and motherboard manufacturers can negatively impact system performance. The impact is different depending on the generation of processor you're running and the method by which the manufacturer implements the fix. Some have found noticeable reduction's in their systems capabilities, while others haven't noticed a thing.
The important thing to remember with these bugs though is that they must be fixed. Spectre and Meltdown provide a very simple attack vector for hackers and systems left vulnerable to it are at real risk of being taken over by a malicious party in the future.