This is just a short tutorial showing how to update your Windows Phone. The tutorial was made using a Lumia 635, but it should work on any Windows phone.
To check for updates on a Windows phone navigate to settings->phone update
The phone update button is found in settings, and has the description get software updates.
When you have found the settings menu you may find it difficult to find what you are looking for, but just scroll slowly trough the options, and you should eventually find it.
Video of how to update your Windows Phone
The below video shows exactly where and how you can update your phone:
How the update feature works
Normally you should be able to download the update directly on your phone, without having to connect your phone to your computer. Lumia supports wireless Over the Air (OTA) updates, so there should be no need for cables or anything.
Depending on how your phone is setup, it may give you a notification when updates are ready to be installed, this should also include notifications for major operating system updates, such as updating from Windows Phone 8 to Windows Phone 10.
Before you update
Make sure that there's enough power on the phone, or connect it to a charger. If your phone looses power doing an update, it could potentially render it unusable - so be careful!
Optionally you can also choose to enable backups, this can be done in settings->backups, on the screen you will find more settings for backing up your photos, videos, apps and text messages. Etc.