As promised, HTC and Sprint have released Android 5.1 for the Sprint HTC One M9, bringing the device software version up to 2.6.651.11. If you have a Sprint HTC One M9, you can check to see if your device needs the update by checking the software version on the device: go to Settings, About, then Software Version. If your Sprint HTC One M9 has a number lower than 2.6.651.11, then the update should be ready for your device. However, before you go into Settings, About, Software Update, Sprint and HTC caution that you'll need a few pre-requisites first. To start you'll need to make sure that your battery is at least 35% and you'll want to connect the One to a mains charger (and be sure to keep the mains charger attached during the update process). Sprint says that it will take approximately twenty minutes to update the device, which excludes the time taken to download the 2 GB update file - it would also always be recommended connecting to a high-speed WiFi network for the software update package download, rather than a 3G or 4G LTE network. The device will also reboot several times during the update process, which is normal.
If you have everything in order and you are due the update, go right ahead and run it. You can look forward to a number of changes after the update has been processed, some of which come with Android 5.1 and some of which are HTC One amendments, improvements and refinements. The changelog notes that there are improvements to cellular connectivity, both in reducing call drops and improving data performance. The One also benefits from some refinement in the temperature management of the device, which presumably means adjusting the throttling of the Snapdragon 810 processor. There are also a number of improvements made to memory management, which is a part of Google's update from Android 5.0 to 5.1, plus some enhancements made to the camera.
Once the update has run, it is a good idea to visit the Google Play Store and check for application updates, letting the device update these. Depending on the applications on your One M9, this might take a little time, so if you are desperate to get back using the device this can always wait until later. It is also usual for the device to get hot during the software update process as the One M9 is working hard.