Open Steam and log in to your account
Click your profile name in the top-right corner
Select Inventory or Account Details
Check your Steam notifications for a gift message
Open your email linked to Steam and look for a purchase or gift notification
Check your Steam chat/messages for a gift notification from the sender
Go to your Library and look for the new game
Check your Steam Purchase History under Account Details
Look for a gift receipt or transaction marked as a gift
If the game was accepted, it will appear in your Library
If you have not accepted it yet, check your Steam Gifts or Notifications section
Ask the sender for the gift confirmation if needed