After fleeing from Helgen and warning the Jarl of Whiterun of the impending doom that Alduin brings, you are sent to one of the first dungeon areas you are likely to explore in Skyrim, Bleak Falls Barrow. Easily one of the more grand structures that can be explored, Bleak Falls Barrow gives you a fairly good idea of what to expect from the rest of the game and is just challenging enough to test your skills in battle.
This dungeon sets up the Draugr, the importance of the dragon claws in sealing them away so they can't assault the people of Skyrim, and shows the first Word Wall that you are likely to come across and beings the player's journey to becoming the Last Dragonborn
Enemies
Before you even set foot inside Bleak Falls Barrow, you will have to contend with a handful of bandits that lurk outside the main entrance. Depending on the route you take to reach the summit, you may also have to battle with wolves and sabercats as well, though thankfully only one sabercat is found on that particular route. Once the bandits outside have been taken care of, there will be a handful more who are trying to loot the dungeon before you reach the animal pillar puzzle that stumps one particular bandit enough for him to accidentally kill himself.
After solving this puzzle for him, you will be attacked by three skeever that are lurking on a spiral staircase that descends further into Bleak Falls Barrow and are probably the easiest enemies in the dungeon, though their quick movements on the staircase can make them more annoying than anything else. Once you reach the bottom of the staircase and proceed through the hallway, you will have to battle the first real threat: a giant frostbite spider.
While it's not the hardest frostbite spider, their ability to easily poison you can prove to be annoying if you are trying to use power attacks as it will drain all of your stamina. After defeating the spider, you will have to cut down Arvel before cutting him down in another sense to retrieve the golden claw, before proceeding deeper into the dungeon.
At this point, you will only come across Draugr, though if you are a high enough level, you may also have to deal with a Troll just before the dungeon's boss battle. This boss battle is against a leveled Draugr that can use Unrelenting Force and Disarm, so it is best to use magic or ranged attacks rather than melee weapons.
Loot
There's a lot going on inside Bleak Falls Barrow, but when it comes to loot, there is decidedly less to get you excited. In the large, open area you enter into once you first enter the dungeon, there is a locked chest next to the campfire with some gold, though not much else. After this, there isn't anything of worth until you reach the other side of the animal pillar puzzle, where you can find the Thief skill book that increases your Pickpocket level, as well as another chest and some empty Soul Gems.
After heading down the spiral staircase, there will be a bench with a Scroll of Fireball and a leveled Paralysis poison that, unfortunately, is usually too weak to work on the dungeon boss and is best saved for another battle. Just before the spider's lair, there is a mess of spider webs that are hiding another locked chest that is about as exciting as the first one you come across, though can hold some weapons as well as gold.
There's not much of note until the boss room, though there are several jars around the dungeon that holds a handful of Septims that can be worth grabbing if you really need the money. Once you are inside the boss room, there are three chests that are all worth investigating before setting off the boss battle itself. The boss chest is the easiest to see, as it is right next to the Draugr's sarcophagus, though there is also a locked chest hidden behind the word wall, as well as one on the far side of the exit staircase, obscured by a small waterfall.
Secrets & Quests
Aside from some relatively well-hidden chests, there isn't much going on inside Bleak Falls Barrow, as the only reason to come here is to obtain the Dragonstone for Farengar and the first word of power for Unrelenting Force.
However, there are a handful of quests that might trigger inside Bleak Falls Barrow or force you to return here after clearing it for the story quest. If you are a high enough level, you may find Meridia's Beacon inside the boss chest, which will trigger the quest The Break of Dawn, which rewards you with the Dawnbreaker Daedric Artifact when completed and is useful for clearing any Draugr ruin.
You may also be asked to return to Bleak Falls Barrow for radiant quests that task you with clearing a dungeon full of Draugr, such as for the Companions or as a Jarl's bounty request. Bleak Falls Barrow is also one of the many locations you may be sent for the quest Fetch Me That Book!, where the player is tasked with finding a spellbook for Urag gro-Shub in the College of Winterhold.
One of the biggest, and only, secrets inside Bleak Falls Barrow is the appearance of a dead NPC named Thomas. If you are level 18 or higher, the level required to spawn the Frost Troll inside the dungeon, he will appear in the same room as the troll, having apparently fallen to his death while trying to defeat the troll and make a name for himself in Skyrim.