In the Options menu, you can enable two settings that allow you to pause the game when playing solo.

• Auto-Pause: If this is enabled, the game will pause while you are in the in-game menus, viewing the map, the cookbook or the plant registry. 
• Crafting auto-pause: if enabled, the game will pause while your crafting menu is open.

In multiplayer mode, only the host can pause the game by clicking on the pause button in the top right corner (next to the clock) and selecting 'Pause server'. The server will then be paused for everyone. 
Please note that only the host can pause a server!