How do I transfer my Quicken account to a new computer

You just need to install Quicken on the new computer and then copy over your Quicken data file.  If you purchased Quicken from Quicken.com you can log into your account and download it from there.  You should also make sure to log in with your current Quicken ID and password.  This all assumes you are using a current version of Quicken and not an old unsupported version.

See these support articles for more details:

https://www.quicken.com/support/can-i-install-quicken-multiple-computers

https://www.quicken.com/support/how-do-i-move-my-quicken-data-file-one-computer-another