After the fork you need to import these private keys (or the recovery seed words) into a wallet that supports Bitcoin Gold or B2X respectively. Using the wallet of the respective Bitcoin fork, you can freely access your coins. However you don't need to "claim" them or access them right away. As long as you have the private keys you can access your forked coins any time in the future.
Caution: Before importing your wallet into Bitcoin Gold, B2X or whatever other fork, you MUST send your BTC to other addresses. Once you empty your wallet, you can import this now empty wallet into the forked blockchain to access your forked coins.
This step will guarantee any weird behavior like double spend/replay attacks and so on. You just don't want matching keys in both chains before you send them to exchanges.