After having installed Dragonborn and having completed the main quest does the player get ability to summon and ride the Dragons? If so, how do I use it ?

Not that i know off. Sorry to ruin your hopes:D

Wrong place.

I think you can summon Odaviin and then shout again to ride him, but I can't say for sure from first hand experience. I know you can't summon the random dragons you shout down though.

You summon him to get the soul tear shout, he dies once you get it.

You're getting your dragons mixed up. Odahviing is from the main quest. Durnehviir is from Dawnguard.

Oops, there are alot of named dragons, i haven't got that far in Solsteim to ride him.