The way spells work is kinda weird: there's magic spells, miracles, and pyromancy.
You need intelligence for magic, faith for miracles, and pyromancy is basically "free" in that you don't have to level any skill to be a powerful pyromancer. There is a weapon that you upgrade that will buff your pyromancy. So you just pay souls to buff it, and you don't have to spend levels. So a super low level player can have very strong pyromancy. The only thing you'd need to "level" is attunement, so you can equip pyromancy spells. These are also some of the most badass attacks in the game, very powerful... and very useful if you do a lot of farming. Most players build up pyromancy, just because it doesn't really have a negative affect on any build you might be going for. Like I said, it's basically free. So lots of people go that route.
I recommend looking at a faq to wrap your head around it... I don't use a lot of spells, so I'm not that familiar with it all.
edit: I just started a new character tonight... we should team up sometime if start you playing soon. I have hardly anyone to summon. And I'm going to keep her real low level for as long as possible. I'm gonna try and build a character with dual whips (lol) and no bow/crossbow. Hopefully I don't get bored trudging through the early game until I get my whips. I was trying to summon for some speedrun help, but no luck.