The file msgstore.db.crypt15 (or older .crypt14) from the phone's Internal storage/WhatsApp/Databases/ folder (newer phones: Android/media/com.whatsapp/WhatsApp/Databases/). Copy it to this computer first.
Paste your 64-digit end-to-end encryption key (WhatsApp → Settings → Chats → Chat backup → End-to-end encrypted backup).
Don't have the 64-digit key? Use your key file instead (needs root access to the phone).
Your chats and key stay on your computer. We never see them.
Decryption happens in your browser. Turn off Wi-Fi and it keeps working.
On an iPhone instead? Use the iPhone-backup version →