How to record a D&D session on Discord
Discord doesn't record voice channels on its own, so recording your game takes something extra. There are a few good options, and the right one depends on what you want to do with the recording afterwards.
Tell your table first
Before you record anyone, say so. Tell the group when you set it up, and again at the start of a session if someone new has joined. Some places require everyone on a call to agree before it's recorded, so check the rules where your players live. Whatever tool you use, give people an easy way to sit out.
Craig
Craig is a Discord bot built for recording voice channels. You invite it to your server, run its join command in the voice channel, and it records each person to a separate audio track. When you stop, it gives you a link to download the files.
Separate tracks are handy if you plan to edit the session into a podcast or transcribe it yourself, because each voice comes out clean. The catch is that you end up with a folder of audio files, and the notes are still your job.
OBS
If you're already streaming, or you just want one file, OBS can record your desktop audio, which includes the Discord call. Everyone ends up mixed into a single track, saved on your own machine.
It's free and fully under your control. Your computer has to stay up for the whole session, though, and one mixed track is harder to turn into notes because every voice sits on top of every other.
A bot that writes the notes
If you want a recording because you're tired of losing track of the campaign, the audio probably isn't what you're after. The notes are.
That's why I built SCRY. You type /record start in your voice channel, play the session, and type /record stop at the end. Afterwards there's a recap of the session and wiki pages for the people and places that came up, each one showing the line it came from. The audio itself is deleted within 72 hours.
When recording starts, SCRY posts a notice in the server. Anyone who'd rather sit out can react to it or type /scry consent withdraw, and their audio is left out from then on.
Which one to use
For raw audio you want to edit or publish, Craig is the easiest place to start. OBS makes more sense if you're streaming anyway and want a single file on your own machine. If the recording is really a way to keep your notes, SCRY goes straight to the notes.