Logged into someone else’s Apple ID and cannot download any apps

Read this document to learn how to sign out of iCloud --> Sign out of iCloud on your devices - Apple Support

For an Apple mobile device:

1. Go to Settings, then tap your name. 

2. Scroll down to the bottom.

3. Tap Sign Out.

4. Enter your Apple ID password and tap Turn Off. (Read this if you If you forgot your Apple Account password - Apple Support ) 

5. Turn on the data that you want to keep a copy of on your device.

6. Tap Sign Out.

7. Tap Sign Out again to confirm that you want to sign out of iCloud.

Also of possible relevance:

Turn off Find My on your devices and items - Apple Support

If this is not your account and you do not know all the information, you basically gifted the device to the other person when you let them sign into your device. That was not wise. You're dealing with: Activation Lock for iPhone and iPad - Apple Support Get the other person to sign out so you can sign in.

Apple might reset a device if you can prove to Apple's satisfaction you are the owner. However, Apple will not do so if Lost Mode is set on a device which may have been done by a scammer if a person signed into their device with ascammer’s account. Check the requirements and steps at: Activation Lock support request - https://al-support.apple.com/#/additional-support Apple says, "Proof of ownership documentation is required," but does not detail what currently constitutes proof other than it “must include the product serial number, IMEI or MEID.” Apple may typically require the original receipt* issued by Apple or an Apple Authorized Reseller. If Apple resets the device this will give you access to the device but won't restore access to the account used to lock it. There is nothing that can be done to expedite an Activation Lock request.

*Apple recommends you "Keep your receipt after you buy an Apple device" --> Keep your receipt after you buy an Apple device - Apple Support