For the great majority of supported Macs, Apple’s Sierra installer app, downloaded from the App Store, works fine.
There are only two important matters that you should consider when using it. Because it automatically deletes itself once it has completed its task, you will want to make a copy before letting it get on with the upgrade. This is easily done: when it displays its welcome screen, locate the app named Install macOS Sierra in your /Applications folder, and make a copy of it in a safe place. To be really belt-and-braces safe, make a second copy on another drive, such as a USB memory stick.
The other important matter applies to those using Macs which Apple does not officially support for upgrading to Sierra. Some slightly older models are supported if you use macOS Sierra Patcher Tool.
Sometimes the Sierra installer fails. This can occur when it encounters some peripherals, or unusual setups such as a home-brew ‘fusion drive’ consisting of an existing hard disk and an SSD which have been bound together as an LVG using Core Storage. In those cases, the installer may run through the initial step, restart the Mac, and fail to proceed with the rest of the install. It should leave your Mac running fine, but frustratingly still in El Capitan.
If that happens, ensure that your Mac is as healthy as you think it is. It’s a good idea to shut it down, disconnect all unnecessary peripherals such as external drives, docks, etc., then start up in Recovery mode and run Disk Utility there to check the health of your startup disk and volume. Once you’ve done that, restart in normal mode, check that your Mac has the correct date and time (if they’re wildly wrong, that can result in installer failure), and try running the installer again.
A further failed install is best tackled by installing from a bootable USB memory stick. If you love doing this sort of thing manually, Apple has detailed instructions which you will need to tweak for the Sierra installer. For most users, though, it is time to reach for one of the standard tools: MacDaddy’s Install Disk Creator, or DiskMaker X. As far as I can see, they both do the job perfectly well. Although DiskMaker X is not yet delivered by HTTPS, I am delighted to report that Install Disk Creator now is, and in this respect at least has the edge.
Once the USB memory stick has been prepared, leave it connected to one of the USB ports on your Mac (avoid using a USB hub if possible), and restart your Mac with the Option key held down. The Startup Manager will then appear: select the memory stick which you have just created, and press the Return key. Your Mac will then start up from the memory stick, and you can run the install process from there.
Installing from a memory stick like this should be as robust as running the installer app from your startup drive, but it is worth making doubly sure that your startup drive is well backed-up. That also gives you the option of initialising the startup drive from the installer, if a regular upgrade doesn’t work out properly.
(Uodated 7 November 2016 to note secure download of Install Disk Creator.)