You’ll trigger this quest on the third day of Fall. Marnie will send you a letter, asking you for some Amaranth. She wants to treat her cows. Sounds like a plan, Marnie.
This is a relatively easy quest. Amaranth is a crop like any other, and you can purchase it from Pierre’s for 70 gold per Seed. Plant it and it will grow in seven days, which is more than enough time to satisfy Marnie on this first month. It will only grow in Fall.
Harvest your Amaranth with a Scythe once it’s done - be careful not to accidentally fell any plants that aren’t ready - and take it to Marnie at her Ranch, south of your farm. If she’s not there she’s probably on the path between the Ranch and Pierre’s General Store somewhere. Pass it over for a 500 gold reward, via your Journal.