Town Shop becomes available once you complete the tutorial. You can find it by tapping Merchant on the main game screen:
Town Shop updates at 9:00 AM, 2:00 PM, and 9:00 PM your in-game time.
There you can use gold or emeralds to buy EXP Potions (their type and number depend on your team level), Bottled Energy, Dorian's Soul Stones, and various items of green, blue, and purple rarity: