Thanks for the question. To move files from your Time Machine backup to a new Mac, you'll want to utilize Migration Assistant:
(see article for full details and screenshots)
1. If Migration Assistant isn't running on the target (new) Mac, open Migration Assistant (located in /Applications/Utilities/), select "From another Mac, PC, Time Machine backup, or other disk" then click Continue.
2. Connect your external hard drive if necessary.
3. Type in your admin password when prompted and click OK.
4. When the target Mac asks you for a migration method, select "From a Time Machine backup or other disk", then click Continue.
5. Select the Drive, Time Machine backup, or Time Capsule. If you select Time Capsule you will be prompted to enter the Time Capsule password. After entering the password, select the Time Machine backup.
6. Close all other applications on the source Mac, then click Continue to start the migration options.
7. The source Mac will ask you to select items to migrate.
8. You can customize your selection by clicking to open the disclosure triangles.
9. After you click Continue, the Migration Assistant will begin to transfer files to the target Mac. The amount of time that it takes for migration to complete depends on the amount of data being transferred and the speed of the network.