How do you actually use this mod? I can't find how you begin to export your technologies or where to find the list once exported.

Click the button with 3 dots on the right of your in-game toolbar. You should see "Export Technologies" on the list that pops up - click the button to the left of it (or toggle the checkbox on to pin the mod to your toolbar).

A window with a textbox should be displayed which you can copy from (with ctrl+c) and then paste into factoriolab.

Edit: I've added a screenshot to the description which might make it clearer, hope this helps!