I've been watching videos on how to install mods. Every time they install a mod they force update it. Will I have to force update my Minecraft every time I want install a mod?
You don't have to do any forced updates to install mods.
Doing a forced update is just intended to make sure you start from a "clean", unmodded, original Minecraft before you start adding any mods. YouTube mod reviewers do it first for every mod because they're constantly trying new mods, so to make a good review they have to reset Minecraft to "factory defaults", so to speak, before installing whatever mod they're going to review. They don't want any old mods contaminating the review.
If your install of Minecraft is working at all and has never been modded, you don't need to do a forced update at all, though it won't hurt anything (or do anything!) if you do. After installing a mod, you actually want to never force update before installing other mods, since force update is the Minecraft way of uninstalling all mods. Unless uninstalling mods is what you want to do, of course.