How do I open it without breaking it?

It's usually the microswitches. You'll need to order a set of Omron switches like this: https://www.ebay.com/sch/i.html?_nkw=omr... -- mouse type really doesn't matter as they're all wired the same, but look for ones made for Logitech mice. You might need to order ~10 when you only need three, as most sellers insist on selling you 10 at a time in the US, so bear that in mind. It's usually best to do all 3 at once, since one failing tends to mean the others are next.

As far as opening it, look under the stickers on the top and bottom - that's Logitech's favorite hiding spot. Most of the time, I consider mice eWaste when they break, but gaming mice tend to be expensive enough that it makes sense to repair them if the parts are available and you can do it.