This guide should help you find the locations of all stardrops in Stardew Valley as well as teach you how to obtain them. Stardrops increase your max health and energy bars in the game.
A stardrop is sold at the Stardew Valley Fair which takes place on the 9th of Fall and costs 2,000 star tokens.
Star tokens can be obtained by:
Purchase the stardrop after obtaining 2,000 star tokens.
An iron axe is strong enough to cut the log blocking your way to the Secret Woods.
The trickiest part is finding sweet gem berry seeds. Normally, it’s sold at the Travelling Cart located south of your farm in Cindersap Forest on Fridays and Sundays (or night market). They take 24 days to grow in Fall. Therefore, it’s recommended to plant them early or in The Greenhouse.
Carry a sweet gem berry to the statue in the Secret Woods and it should reward you with a stardrop for bringing it something sweet.
Level/Floor 100 has a chest with a stardrop.
Upgrade your tools and purchase better weapons at the Adventurer’s Guild if you’re struggling to climb. The Fortune Teller can be checked for good/bad luck days. Bombs may help but not necessary. During early-game, 5-10 floors should be easy to clear in a single day.
Willy sends you a stardrop in the mail after you’ve caught all fish in the game. The stardrop will not be given if you purchase the fish or let someone (multiplayer) catch them for you.
Keep giving a character you want to eventually marry a gift they love twice a week and on their birthday. Once they’ve reached full hearts with you and you’ve upgraded your house at least once at Robin’s shop, purchase a Bouquet 
for 200g from Pierre’s General Store and give it to your partner.
After receiving a letter from Mayor Lewis, go to the right side of the beach on a rainy day (use a rain totem if you can’t wait) and purchase the Mermaid’s Pendant from a shady guy at the top for 5,000g. Give this pendant to your partner and you should marry them after 3 days.
To obtain the stardrop, you need to maintain max hearts with your husband/wife and talk to them daily. You should eventually receive a stardrop one day from them.
Donate 60 items to the museum and Gunter will reward you with the rusty key on the next day. The rusty key can be used to unlock the sewers. Travel to the sewers and you should be able to purchase a stardrop from Krobus for 20,000g (in multiplayer, each player can purchase it).
Donating all 95 items to The Museum will reward you with a stardrop. Big surprise! This might be one of the toughest challenges you will face in the game.
