The Elder Scrolls V: Skyrim/Before the Storm

This main quest activates after you exit the escape cave from Helgen Keep. For this quest, you will head to Riverwood and speak with one of the persons there, then travel to the Jarl of Whiterun to let him know about the dragon attacks.

Riverwood
Your companion, either Hadvar or Ralof, will travel to Whiterun. Although it's recommended to follow after your companion, you are free to explore Skyrim in its entirety.

On the way to Riverwood, following the path will bring you to the Guardian Stones. Here provides a choice of three - the warrior stone, the wizard stone, and the thief stone. The selected choice will increase either magic, stealth, or combat skills by 20% (with the archery skill being treated as a stealth skill in this context.)

Between the Guardian Stones and Riverwood is Embershard mine. You can optionally explore the dungeon on the way back (if you feel the need for some extra loot, or to get the Clairvoyance spell).

Once you reach Riverwood, meet the associated contact. Hadvar will to the blacksmith (Alvor), or Ralof will head to the woodmill owner (Gerdur). When

While you are in Riverwood, you can head to the Riverwood trader to start the Bleak Falls Barrow quest in order to save a bit of time spend backtracking.

Whiterun
Whiterun is simply to the north of Riverwood, with only wolves on the route. The main route tends to bring you past a giant being attacked by members of the companions, if desired you can attack the giant and talk to the warriors.

When you approach the city, the Whiterun guard will stop you, saying that the city is closed due to dragon attacks. To enter, choose any option other than intimidate. You can also enter the city by getting arrested (e.g. punch a guard then surrender). Once you are in the city itself, you can head to Dragonsreach at the top.

In Dragonsreach, you only need to talk to the Jarl. When you approach, Irreleth will demand why you are present, as long as you mention the dragon attack, she will let you pass. Once you can speak with the Jarl Balgruuf, let him know that Riverwood is in danger (or if you skipped riverwood, say that you're reporting the dragon attack from Helgen).

The Jarl will give you some armor, and will introduce you to Farengar Secret-Fire to start the next quest.