How do you learn to fish?

I have no idea what constitutes upgrade to farming tech?

Look at bottom left corner of the screen, above the text Tech Center it's a symbol looking like some kind of medallion. Click that symbol, and you will find several options where you, in exchange for either Tech points or Lava stones, can choose to upgrade your villagers ability in Research, Farming, Medicine, Construction, and Crafting.

If unsure what benefits you the most to choose first, second, etc, click the little information i. That will tell you more specifically what benefits you will get from each respective upgrade.