This is hard to do. First of all, nothing in known physics supports anything that human lore refers to as magic. Therefore, it is inherently illogical in our world.
However, you can't just put in a fancy spell any time you feel like it's cool and awesome. I find when that happens in fantasy stories, the reader just stops believing. It's hard to get immersed when the protagonist can essentially solve every problem with a spell the reader has never heard of before but conveniently works exactly the way the protagonist needs it to. It's also hard to believe a random collection of handy spells with no clear ties can be learned. This is the one thing that annoyed me about Dungeons and Dragons: the magic has no real theme to tie it all together. Sure, there were schools of magic but there was no clear theme of manipulation of something that made the magic really cohesive. Now that didn't stop me from loving D&D as much as I do. It was just annoying.
I like magic when there's a main theme to it. A good game that I know of that works like this is Unknown Armies. Your character would have a world-view so skewed that you see things most people don't, and hence you manipulate parts of the world with that magic. There are conditions to keeping that magic but with one's world view so skewed, it's usually easy to keep to those restrictions. Another game that has a good sense of themes or worlds of magic is World of Darkness' Mage. Each mage is awakened to the secret ways of bending the world. They can only affect certain aspects of the world around them, but over time master it very well and make friends that have different specialties.
I feel like this helps a world make more sense. There has to be some system that works in the world that allows physics bending magic to happen. Whether you're an Urbanomancer in tune to the city so well you can occasionally have hobos do your bidding, or you have figured out how to talk to the dead while you work at the morgue, a system of bending the rules is easy to get lost into when it comes to story. So that kind of system I'm hoping to use.
Right now my idea is to use nature as a system. Of course this would mean using the four elements: earth, wind, fire, air. But I want to intersperse that with other parts of nature too. Plant growth is something I think would be good to manipulate, and I have to think of some other natural forces that can be manipulated. But all of this will be rather limited as well. On with intense clarity and concentration can one move a substantial amount of earth. Air is the easiest to manipulate, but it takes years of practice before someone can actually knock someone over with wind, let alone several people. Fire is so dangerous that usually mages specialize in it and can't make much use of it until a decade of honing their skill.
One thing I think is dangerous to dabble with is the manipulation of things that have free will. People controlling animals will probably not exist in my world at all. Any kind of mind magic, or psionics (a dirty word to many D&D lovers) will be of very limited power. I will say it will exist in my world, but not as a way to manipulate characters with hypnosis or mind control.
I'm hoping I've got the perfect balance of logic and fantasy going on in my magic scheme. You won't know until I've got the web comic up and running how it's going to take shape, but I hope you readers will think my story is full of epic win.
p.s I got the picture for this blog post here.