So I just joined today and I got a couple of eggs. I'm guessing they need clicks to grow? (Correct me if I'm wrong. Are they automatically added to the nurturing page or do I need to do something? Thanks!

All sylesti naturally grow at a rate of one hour per hour until they hit adulthood (at 648 maturity hours)

Egglings get a bonus +1 to their maturity hours for every 5 (or 6? unclear) correct nurtures

Once an eggling hits 72mh it will enter the Hatching phase, where you have 24 hours to manually interact to hatch it to give it a bonus ("help it hatch" option for bonus HP, "let hatch on its own" button for +1 to one of str/int/dex/agi selected at random, or use philter)

Hatchlings get +1mh for every 4 nurtures, and +1 to their lowest stat for every 8 (with HP calculating by discounting the last digit of the HP number, eg, 300hp gets counted as being 30, and mana not getting any boosts unless all other stats are max)

more here

All egglings and hatchlings are shown in the nurturing grounds of their owner, even if they've been moved to the stables to be put on public sale (or to just be sorted into a stable before they age up), a player doesn't need to do anything to make them show up there

Thank you! That makes a lot more sense :)