How to download music directly into my iPhone?

I recently bought an iPhone 4S, and it's my first Apple gadget. I'm still figuring out how to tweak it and stuff, but one thing I can't figure out is, how do I download songs from iTunes straight into my iPhone?
Is it possible to just purchase music from the iTunes app in my iPhone and have it download directly in my phone?
I haven't managed to buy songs yet, but I'm planning to, as my dad's making a bank account just for that purpose.
Is it possible to not use a computer as a third-party to have music in my iPhone?
I've Googled this tons of times, but the fancy lingo couldn't quite stick to my brain, so I hope your answers would at least be able to be interpreted

Yes if you use the iTunes app on your phone the music goes into your phone and when you sync it into your computer it'll download onto there and if you buy music from iTunes on your computer you can put it onto your phone.

Yep, you can download straight to your device from iTunes. Or you could jailbreak it and use some Cydia app like Mewseek.