This one is a bit complicated, but we'll go through step-by-step. You'll need access to your Signal app and a computer.
In the app, press the menu button and go to Settings.
When in settings, press "Chats and Media".
Scroll to the bottom of the page and turn on "Chat Backups".
This will start the backup process, which takes several minutes.
Be sure to save the passphrase shown when you first turn on backups.
On Android, you can go to the "Files" app. The backup file will be in the main phone memory, in the Signal folder. Once there, download the file to your computer. I usually use Google Drive for this, but pick your poison.
The best option for this as of early 2020 is signal-back.
Go to the latest release, and download the compiled binary for your system.
MacOS will be "Darwin", and Linux and Windows are named normally.
Once downloaded, open a terminal window, and run the following command:
./signal-back_linux_amd64 format -f CSV -o backup.csv signal-YYYY.backup
replacing "signal-YYYY.backup" with the name of your Signal backup download.
This will generate the CSV file that you'll give to the visualizer on the main page.
When you upload the CSV file to the visualizer, you'll be asked for an "Address", and the names and IDs of the conversation participants. The names are just to label the data for you to understand better, and aren't used anywhere else. The address is the Signal CSV's term for "conversation". IDs are numbers that uniquely identify participants in the conversation. If you open the CSV file in a spreadsheet app (Excel, for example), you can look around for some conversations that you want to visualize (the message contents will be in the BODY column). Most conversations will only have 1 ID per participant, but if you switched from text to Signal, or had to regenerate your Signal key, then there might be multiple. You can enter as many IDs as necessary, comma separated, in the input.
Make an issue here, I'll be happy to help/fix it!