There are two ways to play items from your iTunes library using Apple TV (1st generation):
Sync: Have iTunes automatically sync your Apple TV with your iTunes library, so you can play items on your TV even if the computer is turned off.
Stream: Stream items from an iTunes library to your TV. You can stream from up to five iTunes libraries, plus the library the Apple TV is synced with.
To sync or stream, you first need to pair Apple TV with your iTunes library.
For other versions, see Play items in your iTunes library using Apple TV (2nd generation or later).
Make sure your computer is on, and iTunes is open.
On your Apple TV, choose Settings > Computers > Add Shared iTunes Library, and note the passcode displayed.
Click the Apple TV button 
near the top left of the iTunes window, then enter the passcode.
Pair your Apple TV with your iTunes library, if you haven’t already (see instructions above).
Click the Apple TV button near the top left of the iTunes window.
Click a content type (Movies, TV Shows, and so on) in the sidebar on the left and choose your settings. Repeat for each type of content you want to sync.
Click Apply or Sync.
The synced content appears on Apple TV. To play an item, select it.
During a sync, items are added to your Apple TV (1st generation) as space allows, in this order: movies, TV shows, music, podcasts. If you also want to sync photos, they are added last, unless you select “Sync photos before other media” in the Photos pane.
Note: If you play content on Apple TV while a sync is in progress, the sync pauses until playback stops.
Pair your Apple TV with your iTunes library, if you haven’t already (see instructions above).
Make sure the computer you want to stream from is turned on and iTunes is open, then do one of the following:
Stream your iTunes library: On your Apple TV, choose Settings > Computers, then choose the iTunes library you want to stream from.
The contents of your iTunes library appear on Apple TV. To play an item, select it.
Stream photos to your TV: Click the Apple TV button near the top left of the iTunes window, click Photos in the sidebar on the left, choose the photos you want to stream, and click Apply.
Note: While content is being streamed, the computer must remain on (not in sleep mode) and iTunes must remain open.
To turn streaming off, click the Apple TV button near the top left of the iTunes window, and select “Show only the synced items on my Apple TV.”
Click the Apple TV button near the top left of the iTunes window.
Click Movies in the sidebar on the left.
Select the movie you want to transfer.
Click Move.
Important: You must be connected to the Internet to transfer a rented movie.
Do any of the following:
On Apple TV, choose Settings > Computers > Select iTunes Library, select your iTunes library, and choose Disconnect.
Click the Apple TV button near the top left of the iTunes window, then choose Turn Off Syncing.
Choose iTunes > Preferences and click Apple TV. Select the Apple TV, then click Remove Apple TV.
Removing an Apple TV from your iTunes library removes all synced items from your Apple TV and turns off streaming.
Do one of the following:
Make sure your Apple TV is turned on and connected to your network. To check your network settings on your Apple TV, choose Settings > General > Network.
Make sure your Apple TV is paired with your iTunes library (see instructions above).
On your Apple TV, choose Settings > Computers > Add Shared iTunes Library, and follow the onscreen instructions.
Check whether the OS X firewall is turned on (in the Security & Privacy pane of System Preferences, or the Security pane of System Preferences). If it is, make sure File Sharing is turned on for iTunes in Firewall Options.