I saw many programms in Android Market which allow to download video from Youtube. Now I must create programm for download video from Youtube, but I don't know how to do it. Can you help me? Thank you for, anyway.
Well first of all. Stackoverflow is mostly used for question. No one here will write a complete app for you, well the majority will probably not do that.
Second, you might want to look at YouTubes ToS:
you agree not to access Content or any reason other than your personal, non-commercial use solely as intended through and permitted by the normal functionality of the Service, and solely for Streaming. "Streaming" means a contemporaneous digital transmission of the material by YouTube via the Internet to a user operated Internet enabled device in such a manner that the data is intended for real-time viewing and not intended to be downloaded (either permanently or temporarily), copied, stored, or redistributed by the user.
You shall not copy, reproduce, distribute, transmit, broadcast, display, sell, license, or otherwise exploit any Content for any other purposes without the prior written consent of YouTube or the respective licensors of the Content.
So please come back with questions that we can answer.
You should probably check out http://sourceforge.net/projects/ytd2/ and http://www.google.com/support/forum/p/youtube/thread?tid=28e5b81a75f31def&hl=en