How do I retrieve messages from my old iPhone?

Where are you in the process of setting up the new phone? Did you just get it and you want to transfer information? Or have you had it for a while?

Are you using the same Apple ID? Did you have iCloud Syncing for Messages enabled on your old iPhone? If so, see here:

Set up iCloud for Messages on all your devices - Apple Support

If you didn't have iCloud Syncing set up on your old phone, you'd need to back up the old phone and restore the back up to the new phone (which would overwrite everything currently on the new phone).

Well if you have the same Apple ID and haven't changed anything recently the should sync with you new iPhone, though it can take a few days depending on how big your archive is on iCloud.