Skyrim takes place 200 years after the end of the last game, Oblivion.
Because it takes place so far from the rest of the games in the series (both temporally and geographically), there are few characters or locations that are relevant to any of the past games.
That doesn't mean that Skyrim has nothing to offer the stalwart Elder Scrolls fan, though.
The Dark Brotherhood, for instance, a player-joinable group of assassins-for-hire, returns in Skyrim, as do the Daedric Princes (or at least minor shrines devoted to them, manned by their followers.)
Even Alduin, the big-bad of Skyrim shows up in the lore of previous Elder Scrolls games, though the rest of the empire thinks he's the Aedra Akatosh. (He's actually his firstborn son)
If you're looking for a general history of Tamriel, the realm in which The Elder Scrolls takes place, the UESP has you covered there too.
But most of that is ancillary to the game itself. Skyrim was not designed as the 5th game in an ongoing series, but as a game able to stand on its own two feet. Even if you've never set foot on Nirn before, Skyrim will welcome you into its lore all the same!
Once you kill the first dragon for the main quest, random dragons can start spawning. It's the second quest in the main questline, so it won't take you very long at all, and it won't reveal too much about where the main quest is going.
Specifically, the quest you need to complete is called "Dragon Rising".
Best Answer
Yes, it is possible to learn Dragonrend without beating Alduin. However you do have to finish a majority of the main quest.
Dragonrend is learned during the Alduin's Bane quest, where you travel temporarily back in time to see how Alduin was captured the first time around. Once you've completed this quest, there's only four more story quests to finish before you're done.