Why is my new iPhone so slow?

I got my first ever smart phone for Christmas last year (2012)-- an iPhone 4. (Don't judge; it was free from Verizon and we're poor!) It only has 8 GB (which is probably part of the problem). But I've only had it for a few months and it's so slow. I've done all I can think of: turned off programs running in the background, updated it so everything is current, deleted all unnecessary things (pictures, apps, texts… ), there's basically nothing on my phone. Last night I even deleted all the music on it in high hopes of clearing it up. All that makes me think that the problem isn't a storage issue. But then I don't know what it is! I'm technologically savvy, so there's probably something I'm missing. The problem doesn't seem to be the 3G, and it's not the wireless (I use my home wi-fi most of the time, and all the other devices-- including my sister's identical phone-- are just fine). This morning I finally gave up and deleted Facebook as well-- it wouldn't run at all. It would just show me a red banner that said "Network Error" and then shut off and go to my home screen. So sad! So… My phone is all but useless now. Does anybody have a clue what's going on? Like I said, I'm technologically savvy, so if you have advice, break it down in easy terms!

Take it to your carrier.

You may have to uninstall some apps or take the phone back.

I think because of ram

Its single core, get dual core 1gb ram iphone5

Make sure you don't have a ton of open apps running in the backgroup, double tap the home button to see your list. Close those out if you have a ton open!