You don't really need to get all seven to get a good amount of energy, and I find that you are able to play the game without much energy issues at 4 or 5 Stardrops. However, it might be nice to have all 7 if you plan on going down deep in the Desert Mines.
Each Stardrop increases your Energy by 34 points, so you can totally increase it by 238 energy points. You do not physically get an item, and instead you just eat the fruit and increase the energy automatically when you obtain one. Below is the location and a brief guide on how to get each Stardrop Fruit.
1) Reach level 100 in The MinesThe reward for getting to level 100 in The Mines is a Stardrop Fruit, and this is probably the easiest one of them all. Just open the chest at level 100 to get it.
Getting to level 100 in The Mines should be fairly easy since you get an elevator checkpoint every 5 levels. Just dig deeper every day, and you will reach this point eventually. If you have problems, buy a lot of food and upgrade your pickaxe to make life in the mines a bit easier.
2) Get 13 Hearts with your spouseWhen you marry another villager you are able to get a total of 13 friendship hearts instead of the regular 10, even tough it will only show 12 in the menu. You clearly know what gift to give your spouse already since you have obtained enough hearts to get it to marry you, so just keep giving gifts even a little while after you have gotten to 12 hearts, and you will soon get your Stardrop.
Talking with any villager will also increase your friendship level, so make sure to talk to your spouse daily even if you don't have any more gifts to give that week.
3) Bring a Sweet Berry Gem to The Secret WoodsThe Secret Woods in an area that is located in the northwestern part of the Cindersnap Forest just south of your farm. You need to have Steel Axe (or better) to chop up the root that blocks the entrance.
Once in the woods you will see a statue called Old Master Cannoli. This statue asks you to bring him the sweetest thing, which is a Sweet Berry Gem.
You get the Sweet Berry Gem by plating a Rare Seed either on your Farm (takes all Fall), or in the greenhouse (any season, but takes a long time). The Rare Seed is always sold by The Traveling Cart, which is located just next to the entrance to The Secret Woods on Fridays and Sundays.
Once you have the Sweet Berry Gem, return to Old Master Cannoli with the gem as your active item and interact with the statue to get your Stardrop Fruit.
4) Buy it for 2,000 tokens at the Stardew Valley FairThe Stardew Valley Fair is hosted on the 16th of Fall every year, and during this one-day event you can purchase a Stardrop for 2,000 tokens. Getting this many tokens can be a hassle, but it's perfectly possible to do it over several years.
You get a decent amount of tokens from participating in the Grange Display, and winning it gives you 1,000. If you want it all in one year you will need to get another 1,000. The easiest way is to just buy them for 50g per tokens. This means that you will need to shell out 50,000g to get it, or 100,000g if you didn't participate in the Grange Display.
You can also get lots of tokens from playing the mini games, but this is much more time consuming than just buying them.
Once you have 2,000 tokens, head to the Fair Shop located just next to the area that takes you back to your farm / the bus stop.
5) Donate all items to the Museum.Donating every single item to the Museum is probably the hardest Stardrop to get, and possible one of the hardest tasks in the entire game. You need to find 95 different items, including elusive artifacts only found by digging in the mines. In addition you will need to find every book, mineral, and artifact and donate it to Gunther.
Once you have donated all 95 items you can claim a reward, which will be a Stardrop Fruit.
6) Catch every fishThere are lots of different fish in the game, and you will get a Stardrop Fruit in the mail from Willy once you have caught all of them. This includes all the Legendary Fish, all the fish found in special places, and fish found in crab pots.
Once you have caught them all, go to bed and open your mail the next day to get your Stardrop Fruit.
7) Buy it from KrobusThe final Stardrop can be bought from Krobus after you have opened the Sewers. He sells a Stardrop for 20,000g.
If you haven't unlocked the Sewers, donate 60 items to the Museum to get the Sewer Keys.