Simply left-click your user avatar, which is located in the client's lower-left corner, to alter your status:
The status-picker menu will appear. You have four choices:
Online: The same old thing. You'll have a green circle next to your avatar when you're online.
Idle: If you are AFK for a predetermined period of time, you usually convert to idle mode automatically; however, you can explicitly choose it from the pop-up menu. When you manually set idle, you can remain in that state indefinitely in contrast to the auto-idle status.
Do Not Disturb: Do Not Disturb (DnD) will instantly mute any desktop alerts you would typically get and display your avatar with a red circle.
Invisible: You can completely appear offline by setting yourself to Invisible, but you can still use the rest of Discord as usual. This includes sending private messages to your buddies.