Note that you can also transfer data directly from one computer to another computer by copying files to an USB stick (jump drive).

You can copy files like these with Firefox closed to the current profile folder to recover specific data. Note that you should be cautious with copying SQLite database files if you previously had problems.

• bookmarks and history: places.sqlite
• bookmark backups: compressed .jsonlz4 backups in the bookmarkbackups folder
• cookies.sqlite for the cookies
• formhistory.sqlite for saved form data
• logins.json and key3.db (decryption key) for Passwords saved in the Password Manager
• cert8.db and possibly cert_override.txt for (intermediate) certificates stored in the Certificate Manager
• persdict.dat for words you added to the spelling checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other Site Preferences
• sessionstore.jsonlz4 for open tabs and pinned tabs

You can use the button on the "Help -> Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page.

• Help -> Troubleshooting Information -> Profile Directory:
  Windows: Show Folder; Linux: Open Directory; Mac: Show in Finder
• http://kb.mozillazine.org/Profile_folder_-_Firefox

Did you try to use the Sync feature that is built into Firefox (since Firefox 4.0) ?

https://support.mozilla.org/en-US/kb/how-do-i-set-sync-my-computer

That said, you might be better off just transferring your data files directly as cor-el explained, if you haven't already used Sync in the past.

how do i find an old account that is syncing to my phone? I have the sync key but can't remember the user name or password, the email it's connected to has been deleted. but the bookmarks are still syncing to my phone and one is replicating infintiely

The Sync Key was used in Firefox 4.0 thru Firefox 28 versions which connected to an older Sync 1.1 version server was shut down a few years ago. That data is all gone.

The Firefox 29 and later versions received a new Sync server (v 1.5), so the earlier version of Sync (v 1.1) could be kept running for almost a year and a half longer to support the ESR version users and other users who kept using Firefox 28 for an extended period.