Summarize the following:
If you do not have it you can download it from the Play Store or App Store. Tap “Log in”, enter your username and password, then tap “Log in” again. This will display all board lists and their associated cards. This button is in the upper right corner and will open the options menu for the selected board. This button is preceded by a “gear” icon and will take you to another list of options for the board. The board will be archived and no longer made visible to anyone on the team, but its data will not be permanently deleted. You can tap “Re-open” board to undo the action.

Summary:
Open the Trello App. Sign in to your account. Tap a board to open it. Tap the 3 dots icon. Tap “Board Settings”. Tap “Archive Board”.