I could so totally rock modern magic.

Yokuwakaru Gendaimahou has a neat little premise: Imagine, if you will, that you could do magic, without having to fuss about with magic circles, incantations, or midnight sacrifices to ancient and unspeakable horrors. Now imagine that all you needed to do magic was a computer. You can find those everywhere! Should be easy, right?
...Right?
The title translates to something like Properly Learned Modern Magic, or Modern Magic for Dummies, and that's basically what it is. The show's protagonist is soft-spoken Koyomi Morishita, a girl who can't seem to catch an even break. She trips on nothingness, only barely keeps up with her schoolwork, is "bad with machines that have more than three buttons", and generally has horrendous luck when it comes to... well, everything. Sick and tired of being the universe's chew toy, she is ecstatic to discover a flier that promises that with the power of magic, she can turn her life around. She makes the trip to quite possibly the last school of magic still in existance and discovers that...
...any magic she tries to do inevitably turns into summoning a wash pan out of mid-air. Thus begins Koyomi's slapstick journey of self-discovery, along with her best friend, emotionless girl Kaho, 'classical' magic user Yumiko, and her whimsical magic teacher, Misa Anehara.
Now, silly as it may sound, allow me to explain: The American equivalent of the wash basin joke, is the anvil joke. Wash pans are almost always laser-targeted for someone's skull, and Koyomi, to add to the suck-plague hanging over her head, happened to win the Useless Superpower Lottery.

fig. a- CLANG

The show's got charm in spades, from simple-minded Koyomi to her (nearly) irresponsible teacher, to the absolutely adorable puppet show that takes place after the credits- more on that later- everything is fairly light and enjoyable to watch. There is a larger story here than just "Oh LOL Koyomi sux!!!1!!!12", but it really only shows itself at the end of the series when a lot of the little things that were easily ignored over the course of the show become relevant (Kaho learning modern magic but being unable to detect it herself, the true purpose of Christmas Shopper, etc.) and the villains make themselves known at last; though, with the way the series jumps around chronologically at the beginning it's near-impossible to tell until the last arc kicks in and you realize that the last episode you watched is the (extremely inconspicuous) beginning of the final chapter of the story. The ending has a really cool twist that even took me by surprise, but I'm going to be a jerk and keep it to myself.
There are a couple times when it gets a little risque, admittedly, but it makes up for this with how developed its universe is. The show doesn't just say "oh hey, this is magic, go with it", it explains how and why some things work and others don't. This is best achieved through the after-credits puppet show (yes really), where Puppet-Misa and Puppet-Koyomi go over everything the anime introduced but never explained, or do (self-admittedly!) shameless promotions. What's the difference between Classical and Modern magic? What do the episode titles mean? What is a Code, magically speaking? What's on the DVDs? The puppets explain aaaalllllllllll.
Allow me to finish thusly: Yokuwakaru Gendaimahou is a show for the patient. Don't watch it expecting the plot to surface immediately, or you'll be sorely disappointed. Don't watch it because you're looking for lots of action and adventure, because you'll REALLY be sorely disappointed. Watch it because Koyomi is a lovable klutz with a lot of heart, the comedy is often well-timed, the puppets are frigging adorable, or you happen to really like a certain character. Watch it because you think the science of magic is interesting, watch it to laugh at washpans hitting people on the head, but don't watch it expecting a truly deep, engaging experience, because it's not there. It's okay to be shallow, every once in a while, and I think Properly Learned Modern Magic pulls it off pretty well.