Upgrade to iOS 13 gets stuck at the Apple logo and the horizontal progress bar
You may want to read If you can't update or restore your iPhone, iPad, or iPod touch on Apple's website. Essentially, You have two main options.

1. Force restart your iPhone

In other words, force your iPhone to reboot. How you do this will depend on your model of iPhone. Since you haven't specified this, refer to Force restart iPhone on Apple's website.

2. Put your iPhone into Recovery Mode

If you have an iPhone 8 or X follow these steps:


Connect your iPhone to a computer with a Lightning cable 
Open iTunes on the computer
Press then release the volume up button on your iPhone
Immediately press then release the volume down button on your iPhone 
Hold the side button, and keep holding it down till you see the Recovery Mode
screen (this appears after the Apple logo


If you have an iPhone 7 follow these steps:


Connect your iPhone to a computer with a Lightning cable 
Open iTunes on the computer
Press and hold both the side button and volume down button on your iPhone
Keep holding them down till you see the Recovery Mode screen (this appears after the Apple logo)


If you have an iPhone 6S follow these steps:


Connect your iPhone to a computer with a Lightning cable 
Open iTunes on the computer
Press and hold both the Home and Lock button
Keep holding them down till you see the Recovery Mode screen (this appears after the Apple logo)