Chrome
If you are using Chrome to browse Twitter, you need to install an CRX file.
The latest version can be found here.
By clicking on the file, you can download it. After download has completed, visit chrome://extensions.
Once you're there, first of all make sure Developer mode is enabled.
Now you must use Drag-and-Drop to place the CRX file in the Chrome window.
Agree by clicking Add Extension and the extension will be installed.
To view the data collected during the current session, you can click on the small jigsaw puzzle icon in the top right and then select Twitter-Tracking icon.
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Installing the extension locally might not work on Windows or Mac, but only on Linux (see here for more info).
If you are affected by this, please consider trying the Firefox extension.