I've noticed that my friends have the Halloween, Christmas, New Years and other display pictures. I'm wondering how to get them?

What exactly do you mean display picture? Different looks or "skins" for champions?

I assume you mean additional summoner icons? If so, they're obtained via promotions during limited time periods (but are unlocked permanently). See the most recent event, the Lunar Revel (aka Chinese New Year): http://promo.leagueoflegends.com/lunar-revel/en.html

Pretty sure that one's ended, but they've only recently been picking up the pace on adding icons, and I believe each of the events/holidays had at least one icon that you could earn without paying money.