Post information and your experiences with Mog Gardens etc. To access your Mog Gardens just talk to one of the Rent-a-Room help NPC's outside west or east adoulin MH and choose to go to your Mog Gardens.
Official update notes for gardens here:
To do all the introductory tutorial quests you're gonna need a lot of inventory space (or just skip obtaining the items). You can buy and sell junk items directly to the Moogle as well.
Zoning in you get a CS that starts the quest Full Fields. Just check the Garden Furrow and choose to harvest its items, then speak to the moogle for a CS to finish the quest. Automatically begins the next quest: Green Groves. Check the Arboreal Grove and choose to prune the trees then speak to the Moogle for a cs and flagging the next quest: Mining Missive. Check the Mineral Vein and choose to mine it for its items and then return to the Mog. Next "quest" Pond Probing just check the Pond Dredger and choose to raise the net for its items, then speak to the mog. CS starts the quest Coastal Chaos: check the Coastal Fishing Next and choose to raise the net for its items. CS finishes the quest and rewards you with herb seeds. For the next quest Seed Sowing trade the herb seeds to the Garden Furrow and choose to plant them. Speak to the moogle to finish and flag the next quest Flotsam Finding. Go check the Flotsam target and choose to pick it up then check the moogle. Finally he rewards you with a garden worm, grove worm, vial of stone serum, sardine sphere, and a ponze of sardine chum.
Furrow specifies it will take 8 hours earth time for herb seeds to grow and that it can be harvested 3 times.
List of shit quests rewarded:
initial furrow harvest from quest: bay leaves, light crystal, eastern ginger, walnut
initial logging from grove quest: ash log, acorn
initial mining from vein quest: wind crystal, pebble
initial items from pond quest: rusty bucket x 2, elshimo newt, giant catfish, moat carp
initial items from coastal net quest: quus x 2, senroh sardine x 2, rusty bucket, contortopus, mackerel, adoulinian kelp
initial item from flotsam quest: water cluster
Green Thumb Moogle will sell you:
vegetable/fruit/grain/herb/wildgrass seeds, and cactus stems