Updates

In addition to what dialabrain has recommended, C0olstorybro, is your iPhone connected to a good, strong, fast Wi-Fi connection?

You cannot update using Cellular, or even a Hotspot connection (at least not one offered from an iPhone).

Usually on the Update page, there will be information that will help us all know why the «update button» is «greyed out».

Try shutting down the phone then reopen it. Has worked for me.