The game starts with you being led on a horse carriage, your hands bound together with some chains. You can look around, so take the opportunity to admire the scenery. The prisoners will speak to give some background on what is going on. The imperial soldiers have captured some rebel Stormcloaks, along with you and a horse thief (Lokir of Rorikstead). One of the prisoners is Ulfric Stormcloak, Jarl of Windhem, the leader of the rebellion.
You arrive at Helgen. General Tullius, the military governor, is there. You reach the destination. Lokir tries to plead for his life, saying he is not a rebel and was picked up by mistake. The guards instruct you to step forward when they call your name. When Lokir's name is called, he attempts to escape but is unsuccessful and gets shot in the back and killed by the Imperial Archers. The guard calls you next, and this leads to the character generation screen.

After creating your character, the imperial captain leads you away to a group of prisoners. Suddenly there is a loud noise, but the General says it's nothing to be worried about. The priestess reads you your rights before being executed.  The guards proceed to execute the first prisoner, a Stormcloak Soldier. The prisoner is decapitated (don't watch if you are overly sensitive to blood and gore). The strange noise sounds again.

The Imperial captain calls for the next prisoner to be executed - you!  The guard instructs you to step forward to the block for decapitation.  As you kneel over and the executioner is ready to chop your head off with his big axe, suddenly a dragon appears in the sky! He attacks the area with his dragon breath.

Ralof urges you to get up. The gods have given you a chance to escape while the guards are distracted with the dragon, and you won't get another chance. Follow Ralof into the tower. Climb up the spiral stairs. The dragon will pop up when you reach the next floor, get back to avoid its firebreathing. Observe that there is a keep on the other side.

You will now get your first quest: Unbound. Open your quest panel to review it. The quest journal lists your quests and objectives. Select a quest and press E (on PC) to make it the active quest which sends its quest target to your compass and world map.

At this stage there will be only one quest there

I have been captured by the Empire and sentenced to death alongside the Stormcloak rebels. We were taken to Helgen, but before I could be executed a dragon appeared and attacked the town. I need to find some way to escape.

Objectives for this quest:
Make your way to the keep
Enter the Keep with Hadvar or Ralof
Loot Gunjar's Body
(Optional) Search the barrel for potions.
(Optional) Attempt to pick the lock to the cage
Escape Helgen

You can press M to see the quest on the world map. On the world map, locations that you have discovered have light icons, while locations that you have only heard about have dark icons. You can select any location you have discovered to fast travel to it.

Jump through the roof, and keep going. Make your way to the keep across, watching out for dragon fire. Then enter Helgen keep with Hadvar or Ralof. Your objective now is to escape helgen.

In the keep, it seems like you and Ralof were the only one who made it. Approach Ralof so he can cut your hands loose. You should take Gunjar's gear since he won't be needing them anymore. Search the body of Gunjar to find a Iron War Axe, a Stormcloal Cuirass, and fur boots. Take them all. While Ralof is looking for a way out, open your inventory (On PC, press I or TAB) and put on the armor and boots, then practice swinging the axe.

The Imperials will show up! Take cover. They will open the gate and go in. Kill them. Ralof will find the key on one of the soldier's body. Search both soldiers and grab all the loot.

Ralof will open the gate. Follow him down the stairs. The dragon is still around. Enter the store room. Kill the soldiers in there and grab some potions. There will be a potion of minor healing on the wooden table, as well as a potion of minor magicka on the shelf. Take anything else you run across, you can sell the items later.

Once you are done, go to Ralof and follow him down another stairway. You will reach the torture room. Some guards are torturing prisoners. Kill the guards.

On the table there will be "The Book of the Dragonbore". You can read it for some lore. Take it afterwards.

Search the knapsack to find some lockpicks then use them to pick the lock on the cage. To lockpick, use mouse to rotate the lockpick then press A to rotate the lock. The closer the pick is to the correct position, the more the lock will rotate before the pick breaks. Only when it is in the correct position will the lock fully rotate and open.

Once you are done picking the locks, keep following Ralof. You will get to a big chamber, kill the Imperial Soldiers inside.

Use the lever to lower the drawbridge ahead. There is no going back after this point, so if you still want to loot stuff or explore the previous area, now is the time.

Cross the drawbridge. Keep following Ralof along a small stream of water, and into some caverns. There will be some Frostbite Spiders here, kill them. As always, search all corpses you kill for loot.

At the end of the cave there will be a big bear! Ralof recommends either sneaking around, or using the bow to surprise her. Practice sneaking around the bear, follow onscreen prompts for instructions. Watch when you are hidden, and when you are detected. Ralof will follow your lead..

Finally you reach the exit. Go out, and you will find yourself outdoors, in Skyrim. Talk to Ralof. He tells you that the area will soon be swarming with imperial soldiers, so you should leave the area as soon as possible.  His sister Gerduf runs a lumbermill in the nearby town, and she will help you out. You split up, both going in your own way. You should now follow Ralof's advice and head to the town of Riverwood.

This completes your first quest, and also unlocks a trophy/achievement: Unbound