Generally speaking, HTC smartphones are relatively easy to root/unlock, especially if they are unsubsidized by the carrier. We've owned 4 of them in the past 5 years, rooting is not as difficult as it sound. Read & follow the detailed steps and directions, backup the data on the device first and store them safely first before making changes. When in doubt, don't rush & post the questions on XDA first - use the Q&A subforum for HTC One after searching FAQ and prior posts by others, might've been addressed and with tips & cautions, etc.

Here's a shortcut link to XDA-D for the "HTC One 2013" a/k/a "M7" model, please check & make sure it matches yours - as there are some variants for the HTC One, depending on country and/or carrier spec's
http://forum.xda-developers.com/show....php?t=2281365

It's important to identify your model so that you can do it correctly and not get boxed in, as most can usually be flashed & restored to factory state - stored data could be 100% lost (thus, backup - backup and backup)

If you have a spare/backup or bench/test computer, use that to do the work - the actual time might be as little as 5 minutes, planning & understanding is time consuming. The 3 basic steps are:
a) unlock the bootloader (HBoot)
b) flash a recovery image
c) root the device

The device will erase and reset, but once it's done correctly, should reboot again and you will need to setup again to enjoy it. Learn how to get into your custom recovery, and wipe Cache and Dalvik Cache properly. Wipe System or Sytem Reset command is much more "dangerious"

Flashing a custom Rom is optional, the factory Rom can be used as is. There are "Toolkits" as one-click solutions, automated for dummies - try to avoid using them unless all else failed.

Google in Youtube as there should be video demo on how to root the "One"

If you aren't comfortable doing this, consider doing a Master Reset first, after backup all your important data & settings first. It might or might not help "fix" your problems but worth a try, before rooting it, etc.