On this page of the guide to The Elder Scrolls V: Skyrim we have presented a walkthrough of the initial part of the main quest Before the Storm. Our step-by-step guide, tells you how to get to Riverwood and where to find Alvor, with whom the main character must talk.
New main objective: Talk to Alvor in Riverwood
Note! You will receive this objective only if during the Unbound main quest you decided to befriend with Hadvar. If you allied with Ralof, head to Meeting with Gerdur.
Open the map to establish that Riverwood is north of the Helgen Keep exit (screen above). You of course don't need to head there following a straight line, as you can stay on the main path as well. As for Hadvar, even though you will theoretically temporarily split up, you should follow him and stay nearby.
On your way, I'd definitely suggest stopping by the Guardian Stones (screen above). You should interact with either one of the Thief Stone, Mage Stone or Warrior Stone. By doing so you will receive a blessing and increase your skills in a given field by 20%.
Keep heading north and be ready to fight off some Wolves (screen above). If Hadvar is nearby, the fight should be very easy. Otherwise, you will have to be very careful and remember to attack the wolves one at a time. Afterwards examine their bodies and head towards Riverwood.
After reaching Riverwood, approach Alvor and listen to a short conversation between him and Hadvar. Afterwards head to the door leading inside the Alvor and Sigrid's house (screen above). Some more talking awaits you there. Note that Alvor offered you a number of free items which you should of course move to your inventory. In the further part of the conversation, you will learn of the need to meet with the Jarl of Whiterun and inform him of the Dragon's attack, so that he send in more soldiers to Riverwood. Before heading out, I'd suggest talking with all the NPCs, asking them additional questions. The further description can be found in Going to Whiterun.