There will be a Discord chat by the name of “your tournament-request” or "YourRegion-request". This channel usually opens around 2 hours prior to the start of the tournament in question. Depending on which tournament you are competing in, the request channels can be located under different categories in the channel list. Generally, the category will be named something similar to the tournament name. Daily cup request channels will be located under the category named "Dailys Europe / Americas" for example.
In said chat, your team captain needs to write ONE message (the instructions on what exactly to write will be announced in that same Discord channel. Generally, this message requires you to state ! followed by your group name. !bravo or !group1 for example.
If your group request is approved, either the Discord bot or a GLL admin/ community moderator will react to your Discord message with an emoji. If the bot approves it, it will react with the lvl3lul emote. Admins reactions may wary, but if an admin has reacted to your message with an emote you can know that it has been taken care of. (Admins and community mods are listed in the right sidebar on Discord.)
If for some reason you do not gain access to the requested group, send a private message to one of the GLL Community mods or admins, and they can help you get the correct role added.