On Xbox, you can claim access on the Microsoft Store; PlayStation users will need to visit the PlayStation Store. PC players can claim their free week on the Battle.net launcher by opening the client, clicking on the "Call of Duty: BOCW" title and then clicking the blue "Try For Free" button on the right of the screen (pictured below). The game is also cross-platform compatible, so you can play with your friends from any platform!
Remember, trial access only lasts until the 21st January. If you want to get involved, you'll have to act quick!