In the previous chapter, you found Gerdur in Riverwood and she agreed to help you with some food and shelter. In return, she said she would appreciate it if you could do her a favor.
Open your quest journal, and you will see that the quest has been updated:
Ralof's sister Gerdur asked me to take word of the Jarl of Whiterun of the dragon attack on Helgen, and to ask the Jarl to send soldiers to protect Riverwood.
Your goal now is to talk to the Jarl of Whiterun
As Ralof and Gerdur leave, feel free to talk to Ralof. You can ask him where Whiterun is ("to the north") and ask him about what happened back in Helgen, why he was captured, and whether the Dragon was on his side or not. This is purely optional and it adds to the story. Ralof will also ask you again to join the Stormcloak Rebellion in Windhelm. They need fighters like you.
First though, there is something you need to take care of. You have probably amasseud items in your inventory. Especially if you are like me who loots first, and asks questions later. You want to sell stuff you have in order to make some gold as well as clear space in your inventory. Open the map, and locate the Riverwood Trader.
Enter the shop, you will see the merchant arguing with Camilla. Upon inquiring, you learn that the shopkeeper has some problems with Bandits. This unlocks a quest, "The Golden Claw". If you talk to Sven earlier, he might have given you a letter to deliver to Camilla, you can talk to her and complete that objective.
Barter with the shopkeeper, selling him the items you dont need and buying items and spells that are useful to you. If you look through his inventory you will see he mas many useful items. Some of them will be too expensive for you at this stage, so you will have to come back and buy them later. It is best to take this chance to unload as much weight as possible, so you will be able to carry loot from the quests ahead and make more gold.
Also, around this point you will be leveling up. Whe your level increases, you must choose to increase your health, Magicka, or Stamina. You can also select a new perk at this time, or save it for later. Available perks are highlighted in each constellation.
After finishing any business you have in the town, head NE to the edge of town and cross the bridge. You will arrive an a signpost. Follow the sign to Windrun, and head Northeast on the paved path, paralled to a river. Soon you should see Whiterun on the horizon. Keep following the road. It will take you over the hill. Reach a bridge and a signpost. Do not cross the bridge. Instead, turn left, following the sign. Go past the brewery and past Pelagia farm. Keep following the signs to whiterun, running right at the next junction. There is a carriage near the whiterun stables that will take you to any capital, can prove useful later, but for now go past it.
Go north and enter the keep through the gate. Cross a drawbridge. You will be stopped by a guard who will tell you that the city is closed because of the dragon, except for official business only. Tell him that Riverwood calls for Jarl's aid and he will let you through. Go to the big wooden door and enter Whiterun. On the way to Jarl, feel free to talk to the townspeople, look around in the shops, and barter with merchants. There is some dispute going on between the Gray-Mane and Battle-Born family. In the market, you can overhear a conversation between Fralia Gray Mane and Olfrid Battle-Born regarding Fralia's son who is missing. The Battle-Born claim her son betrayed the empire and died as a Stormcloak Traitor, while Fralia says they are lieing and that her son is still alive. Talk to Talia after the Battle-Born leave to receive the "Missing in Action" quest.
From the market, climb up the stairs to the North. Make your way up the keep, and enter Dragonsreach. Approach Jarl in his throne. Irileth will ask you why you are here. Tell her that Gerdur sent you, Riverwood is in danger. She will ask you to tell her the message, but refuse and say your message in intended for Jarl. Jarl will hear this and ask what you have to say about Riverwood being in danger. Tell him that a dragon destroyed Helgen and Gerdur is afraid that Riverwood is next. Jarl will ask you if you are sure Helgen was destroyed by a dragon and it wasn't a stormcloak raid gone wrong. Tell him what you saw. Irileth will suggest Jarl sends troops to Riverwood. Jarl will issue the order to send a military detachment to Riverwood.
This completes the quest, and Jarl gives you a reward. He also wants you to follow him so that the two of you can speak to Farengar, his court wizard. There is something he needs your help with. This starts the next quest, Bleak Falls Barrow.