Where is the quests/where are the trainers Follow

I'm not quite certain on what your question is, because I don't know where you are, or even whether you've finished all the Death Knight starter quests. Basically, in the starting area, there isn't an inn. It's instanced, but since you aren't able to leave the instance, there is no summoning stone. If you still have starter quests to finish, then you MUST finish them. They aren't optional, like later quests, and you don't have the choice to abandon them and continue the game.

After you've done all the starter quests you can go where you want, and if you go to an inn ask innkeeper to bind you to that inn you'll get a hearthstone from him.
The only DK trainer is in the starter area but you get an ability to transport you there, and then hearth or fly back.

Use the Death Gate spell to return to Ebon Hold for your DK-specific training. Ask any inkeeper you like to set your hearth point there for you, and they give you the Hearth Stone. For any other skills you need, just see regular trainers.

To summarize the above in concise fashion:

1) Finish all the quests in the starter area. Yes! ALL.
2) Final quest in starting sequence sends you to see the leader of your faction. You are ported to Stormwind for Alliance. Og if you are Horde.
3) On your way to see the ruler, you will be spit on, have rotten fruit thrown at you, etc.
4) Talk to the ruler and "Bob's your uncle!", you are neutral with you sides factions.
5) Now you can seek out the trainers whose professions you wish to learn.
6) A Hearthstone can be attained by asking any Inn Keeper to bind you.
7) The only DK trainers are in Acherus. You can use your Death Gate spell to get back there at any time.

As a side note, many, but not all, flight paths are also mapped out for you.

Good hunting!

Magestar - 70 Gnome Mage
Phestering - 62 Drenai Death Knight
Both of Medivh