As you pass through Riverwood many times on your journey through the main quests of Skyrim, you’re apt to spend some considerable time there. It also is the first village you will actually interact with (Helgen both being more of a fort and also destroyed before you really get to see any of it) and therefore it is here you will most likely first go and talk to an innkeeper. Orgnar runs the inn here with his wife Delphine- she handles rooms, and he handles drinks, food, postings by the Jarls, and gossip.
Orgnar (or any innkeeper of your choice) gives you four of the seven ‘miscellaneous’ quests you can get in Riverwood.
He will mention the College of Winterhold, giving you the spur to start that questline.
He will point out the existence of the Shrine of Azura, which you ought to go see.
He will explain that there are rumors of some kid named Aventus Arentino trying to get the attention of the Dark Brotherhood.
He will also pass on to you (as will any other innkeeper in Whiterun Hold) a bounty on the bandit leader at Redoran’s Retreat.
Sven, the local bard (and any other bard you care to run into and ask about their profession) will point you at the Bard’s College in Solitude.
These five quests are all the starts of large questlines and will be covered later.
The last quest from Riverwood is the Riverwood Love Triangle. Sven the bard, and Faendal, the elf who helps Hod and Gerdur with the mill, are both after Camilla, the sister of the man who runs the trader’s shop in town. Whichever one you talk to first will give you a letter. He wants you to give this letter to Camilla and tell her it’s from the other one. If you like, you can bring the letter to the other suitor, who will act outraged and then give you the exact same letter they would have given you if you had spoken with them first. You then talk to Camilla, and you will give her the last letter you were given.
If you choose to tell her the letter was from the person whose name is on it, she will thank you and the person who gave you the letter will as well- and pay you 25 gold for your trouble in addition to being available for you to have as your Follower.
If you choose to tell her the letter was from the person who actually gave it to you, she will thank you and the person who didn’t give you the letter that you gave her will, again, thank you, give you 25 gold, and become available to you as a Follower.
Curiously, you cannot ever give her both letters, regardless of whether you intend to lie about their origins or not.