Step by Step: Uploading an Emoji
On desktop or the web, open the server menu by clicking the server name, choose Server Settings, then Emoji, and click Upload Emoji. You can select several files at once. On the mobile apps, open the server, tap the server name, go to Settings, then Emoji, and tap Upload Emoji.
After uploading, Discord shows each emoji with an editable name. Rename them before members start using them, because renaming later breaks people's habits. If a file is rejected, Discord shows an error next to it, usually because the file is too large.