Step 1: Join any Mario Kart Wii Discord with war chats in it. If there are specific sizes in the chat titles, ask in the chat for the size you want.
Ex: #war-chat (specify size and track type), #rt-5v5 for 5vs5 on regular tracks only, #rt-3v3-4v4-6v6 for 3vs3, 4vs4, or 6vs6 on regular tracks only.
Step 2: Wait for someone to say "can" to you (note: this can take a long time because of the existence of Mogi Lounge).
Step 3: Organize the rest of the war within Discord Direct Messages with that person.