Stardew Valley

The smaller details (such as heart score) of this guide are taken from http://stardewvalleywiki.com/Friendship

Your friendship level with most villagers is represented by a ten heart meter.
Villagers you can marry have their last two hearts locked until you reach 8 hearts and give them a certain gift (bouquet). Until the bouquet is given their heart meter is considered full at 8. As long as you are not married, you can give the bouquet to as many villagers as you like with no negative repurcussions.
Marrying someone will unlock two extra hearts plus an additional hidden heart for a total of 13.
Each heart is worth 250 points.
Certain actions/inactions increase/decrease your heart points with the villager in question.

Increases score:
+Talk to them (+10-20)
+Making certain decisions in heart events
+Completing a quest for someone (+150)
+Giving them gifts (love +80, like +45, neutral +20) This score is multiplied by 8 on the villagers birthday and by 5 on the secret santa event. The quality of the item gifted also affects the score
+Dancing with one of the bachelors or bachelorettes at the Flower Dance festival (+250, but need 4 hearts before they will accept to dance)
+Adding the right ingredient to the soup at the Luau festival (+120/60 with everyone)
Full list of good and bad ingredients can be found here: http://stardewvalleywiki.com/Luau
+Completing all bulletin board bundles at the community center will raise the player's friendship rating with every non marriage candidate villager by two hearts.

Decreases score:
-Not talking to a villager (-2/day)
-Hitting them with the slingshot
-Going through a trash can when seen (-25, but Linus doesnt mind)
-Giving them gifts (hate -40, dislike -20) This score is multiplied by 8 on the villagers birthday and by 5 on the secret santa event. The quality of the item gifted does NOT affect this score
-Adding the wrong ingredient to the soup at the Laua festival (-100/50 with everyone)
Full list of good and bad ingredients can be found here: http://stardewvalleywiki.com/Luau

You can only give a villager one gift/day and a maximum of two/week (you can always give a gift on someones birthday, even if you reached that weeks max).

Once you reach 10 stars (8 with romanceable villagers) it will not decrease if you ignore them. It can still decrease with bad gifts/actions.

Listing every characters loves/likes etc would take up several pages of text so i will instead link to where you can get that info: http://stardewvalleywiki.com/Villagers
Just click on the desired villager to see details of what they like and also their schedule for moving around.

Have fun out there and remember, no sex before marriage!
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Thanks to contributors:
ALollz
Kelle1994
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Writing guides/solutions is about helping the community, a lot of time can go into writing some. Thats why i wish that if you dont find the guide helpful you will leave a comment and tell the author what you dont think is correct or what might be missing so we have a chance to improve it for the next person who reads it. This way you help the community as well. Thanks!

Zordnil's solution is great for explaining how the heart system works in Stardew Valley. However, it does not really explain the fastest way to get all of the heart related achievements. The easiest and best method, in my opinion, to get this achievement is to get the recipe for Sashimi.

First, you must have an upgraded house with a kitchen. This will cost you 10,000 gold and 450 wood. The best way to get this is to fish nonstop and cut down trees in the forest south of your house. While doing this, you can start working on getting the actual recipe unlocked.

The Sashimi recipe can be obtained by reached a three heart level friendship with Linus, the man who lives in the tent to the north east, right next to the mines. You can give him many things, but the easiest would be yams in the fall because you can grow them. Note that you can only give him two a week, so either continue playing normally or sleep until the next week is available. If it is the third of winter, you can give it to him for a huge bonus as this is his birthday.

After you have a three heart friendship with him, he should send you the recipe the next day through the mail. All this recipe requires is one fish. So the whole reason behind making money with fishing is that your fishing level will be higher, which will let you catch fish easier. Also, you can purchase bait from Willy at the beach for 5 gold a piece if you have the Fiberglass rod (which will cost you 1800 gold at Willy's shop).

Once the recipe is obtained, all you have to do is fish and fish all day, then go into your kitchen and turn it into Sashimi. This meal is loved by Sebastian and liked by everyone but Willy, Emily, Evelyn, Kent, and Krobus.

So, essentially all you have to do is make sure that every week you give 2 Sashimi to the villagers you have decided to use to get this achievement. Remember to give them it on their birthday as well and you will have this achievement as well as all the other heart related achievements in no time.