how do I transfer the content from a dead computer to a new computer

From its Time Machine backup. Refer to Transfer your data to your new MacBook Air.

You don’t give enough information to allow a useful answer. For example, you need to say which model of (dead) MacBook Air, which might help identify whether the old storage can be removed from the failed machine, and which specific adaptors might be needed to connect to a new machine for transfer. Then there is a potential problem with passwords and/or encryption, depending which version of MacOS it was using.

With all the potential problems of transfer from the old hardware I think your first approach should be to look for a recent backup which may be easier to restore without heroic surgery on the old machine. If you don’t have a backup and you need to ask the questions here it suggests you might be struggling at the limit of your ability to do a “technical” recovery of your data. That doesn’t mean you should not try, but be prepared for failure.