What i need to write to start a quest in the script box "Papyrus fragment" in the topic info box?

1. Just type in ";" without the quotes and click the compile button. You'll see a fragment script being generated.
2. Click the fragment script and click "Properties". If the "add property" button is grayed out, go back to the dialogue view and make sure your dialogue is actually linked.
3. Add a Quest property. Set it to your quest you want.
4. Erase ";" and type in myquestproperty.Start()

Excuse me, but linked to what? And how i link it?

Much simpler way:

GetOwningQuest().SetStage(10)

Stage 10 might not be the starting stage of your quest.
In general this tutorial is really good: http://www.creationkit.com/Bethesda_Tutorial_Planning_the_Quest

But how I active a specific quest?

Have you followed the tutorials on the wiki? http://www.creationkit.com/Bethesda_Tutorial_Dialogue. If the dialogue is working ingame then good, just add a quest property for the quest you want to start. Then in the fragment box all you need to do is questpropertyname.Start()