Here are some of the mod I am using in Stardew Valley. Some add features to the game, make things a little easier, or are just for fun. If you would like to get started modding your own game, feel free to check out some of these mods. There are many, many mods for this game. My recommendations are a good starting point, but once you start modding you can find other mods that fit your own play style.
Before I get into specific mods, I have to mention SMAPI. You will need to download SMAPI first, as it is a prerequisite to most other mods. SMAPI is a mod loader that allows other mods to run when you launch Stardew Valley.
The installation for SMAPI is relatively easy and can be completed by anyone with slightly more than "beginner"-level PC experience. Instructions are included and there are plenty of resources to help online. If you use Steam, I highly recommend you follow the options to "configure Steam", it makes it very convenient to launch the modded-version of Stardew Valley directly from Steam.
These mods include useful utilities that add helpful functions or cheats to the game.
Mod Update Menu - This mod adds a menu to the title screen that will let you know if any mods need updating. You can see if mods need updating from the console upon booting the game. However, I find this mod to be a little more convenient. It even includes links to the mod download pages.
Lookup Anything - Lookup Anything is a very useful
CJB Cheats Menu - Adds a cheat screen to the in-game menu. There are tons of cheaty things you can do here.
CJB Item Spawner - Let's you spawn any item in the game!
CJB Show Item Sell Price - Simple mod that lets you see what the sell price is when hovering over an item in your inventory.
NPC Map Locations - Shows the location of all the NPC characters on your map.
Enemy Health Bars - Displays a health bar above enemies. By default, it will only show on certain enemies based on your combat level and the number of that type you have killed.
AutoWater - Automatically waters all of your crops.
Running Late - A simple clock mod that shows each minute of in-game time passing (as oppose to updating every 10 minutes).
Content Patcher/Json Assets
Content Patcher - The Content Patcher is required for many of the following mods to function.
Json Assets - Allows modders to easily add items to the game with minimal programming knowledge. The wiki for this mod seems to be dead, but this Blank Json Assets Template is a good place to start if you want to make your own content pack.
Coffee Maker (Requires Custom Farm Redux & PyTK)