How can I transfer my old Apple ID to my new Apple ID

You can't merge multiple Apple ID accounts.

I forgot most of my sign in details on old phone

Check your Apple ID via your email box, see this Apple article: If you forgot your Apple ID

If you forgot your Apple ID email address or phone number - Apple Support                  

OR see -> Having trouble signing in?

https://iforgot.apple.com/password/verify/appleid

If you've forgotten your Apple ID email address or phone number

If you've forgotten your Apple ID email address or phone number – Apple Support (UK)

See -> If you can't connect or sign in to iCloud

If you can't connect or sign in to iCloud - Apple Support

Have you forgotten the password? -> See this Apple article: If you forgot your Apple ID password

If you forgot your Apple ID password - Apple Support

Then see this Apple article: What to do after you change your Apple ID or password

What to do after you change your Apple ID or password - Apple Support

See if anything here helps                   

Transfer content from an iPhone, iPad, or iPod touch to a new device.    *

ASC YouTube for how transfer data to a new iPhone

 Quick Start to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch.  *

 Use iCloud to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch   *

Set up your iPhone, iPad, or iPod touch - Apple Support.   *

ASC YouTube for how to set up a new iPhone