This is the final quest in the main quest line. Before you head off with Odahviing, be sure you stock up on potions (especially Fire Defense, Health Restoration, and any potions that buff your primary attack method)
FULL DISCLOSURE: In my playthrough, I had my character maxed out at 100 for Archery, Smithing, and Heavy Armor. I had her equipped with a full set of Dragon Bone armor and a Daedric Bow.
After arriving in Sovngarde, you'll need to make your way through the mists to the Hall of Valor. Once you arrive at the bridge leading to the hall, you will have to fight a guardsman named Tsun to prove that you are worthy to enter. During this fight, you'll only need to take him down to around 3/4ths life before he concedes and allows you to enter.
Inside, you'll need to speak to the three Nord heroes, Gormlaith Golden-Hilt, Hakon One-Eye, and Felldir the Old, who you saw fighting Alduin after opening the Elder Scroll. Upon speaking with them, they will lead you outside and back across the bridge where you will need to do the Clear Skies shout three times before the real battle begins.
As Alduin comes closer be SURE to equip the Dragonrend shout, as it's the ONLY way you can harm him. When Alduin goes into "hover mode", hit him with the shout to bring him to the ground.
With my character being an archer, I downed my best "archery buffing" and fire defense potions, and made sure to have health potions at the ready. I also equipped the Daedric Arrows which I had been hording for the big battle (and held Ebony ones at the ready).
Once Alduin lands, try to move yourself out of his line of fire and attack away, strafing around him. If you DO get caught in his fire breath, keep an incredibly close eye on your health meter, as it will drain faster than you imagine.
Continue plugging away while he's on the ground. Once he lifts off again, heal up, bide your time, and wait for him to enter "hover mode" again before hitting him with Dragonrend and continuing your attack.
When I entered the battle, my character was at Level 50, and I didn't have too much of a problem.