When you come across the items which you need to ask from friends, you will see a blue 'Ask friends' button. You should click on it, and you will see your friendlist with buttons 'Ask' for your neighbors and 'Inform' for the friends who don't play the game yet. When you click 'Ask' you will get a pop up window asking whether you agree to send your friends a notification about your request. If you don't want to see this window again when you ask this friend, just check the box near the "Don't ask again before sending requests to -- from this app" message.
If you've already asked a friend for an item, 24 hours must pass before you can ask him/her again.