Assuming you've made it to our general channel, you should be able to use our emotes immediately. If this isn't the case, follow these steps.
Refreshing your client is the easiest and fastest solution. If you don't know how, continue reading.
Press CTRL+R to refresh your client.
Press ⌘+R to refresh your client.
You know the refresh keyboard shortcut.
Open the app switcher to close and re-open the Discord app. If this method does not work, you may have to log out and log in again.
Refresh the website.