Activating the quest
Quest requirements: This mission can be completed at any point in the game. As it includes at least one remanding fight, it would be good to wait with it until you develop your hero sufficiently. Also if you don't want to encounter any additional difficulties, I'd recommend completing this quest before you unlock the ability to change into a werewolf.
Start off by heading to Falkreath. It can be found in the southern part of the map (screen above) and if you haven't discovered it, it would be best to start at Riverwood and head south-west.
This quest can be activated in two basic ways. The first implies heading to the northern part of Falkreath. There you should find a rather big cemetery and witness the end of a burial ceremony (screen above).
After the ceremony, approach Mathies and speak with him about the deceased (screen above). the man will tell you that his daughter was brutally murdered by a certain Sinding, who's at the moment at the local prison. Note - if you don't come across anyone during your visit to the cemetery, you had probably already activated the ceremony during one of your previous visit in the town. In such situation, search for Mathies on the field adjoining the Corpselight Farm.
The second way doesn't imply speaking to Mathies at all and heading to talk with Sinding, the man accused of the brutal murder (screen above). Details on reaching Sinding and the course of the conversation can be found in the description of Talk to Sinding main objective.
New main objective: Talk to Sinding
You can meet with Sinding regardless of whether you spoke with the father of the murdered girl or decided to skip it (you don't lose anything that way). Head to the south-east part of the village and find the entrance to Falkreath Barracks (screen above). after getting inside, head towards the door leading to Falkreath Jail.
Don't start a fight and turn left, heading to the northern call. Wait for Sinding to approach you and speak with him (screen above). He will tell you that he's a werewolf and he murdered the girl by accident. The man has a cursed ring which causes the transformation to be completely random.
In the end you can of course offer to help Singing, taking the Cursed Ring of Hircine and heading out to find the Lord of Hunt who can take off the curse. The first part of the plan implies slaying a majestic beast, which supposedly guarantees an audience with Hircine.
Gaining an audience with Hircine
New main objective: Kill the great beast
Before heading out to hunt, you should know of a certain difficulty. The ring you got from Sinding will be automatically equipped and you won't be able to take it off until the end of the mission. If you character already had the ability to change into a werewolf, you must keep in mind that while wearing the ring it could happen at any time. As a result it would be good to leave Falkreath as soon as possible to minimize the risk of scaring its citizens. I'd also recommend taking care of this mission as fast as possible to take off the curse. You can of course use the random transformation to your advantage as well, though don't forget to put on your equipment back on after returning to normal.
Open the world map, thanks to which you will establish that the beast pointed by Sinding can be found in the woods east of Falkreath (screen above). it's best to go there on foot, especially that it's quite nearby.
After locating the target it will turn out that you're not meant to fight any sort of monster, but kill the White Stag. It's best to attack from a distance, using a bow or spells (screen above). Though be sure to kill it at once.
If your hero prefers direct combat, it will be much harder to hunt down the stag, as the animal will start running immediately upon noticing you. In such situation you should make use of your powers, for example the Unrelenting Force Shout (screen above).
Regardless of the chosen method, you must approach the dead stag and the Aspect of Hircine will appear. Speak to it (screen above). The Daedric Lord will want you to hunt down Sinding and in the end skin the werewolf. Whether you agree to refuse doesn't matter, as you will be able to continue the quest either way.