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I've got zero experience with drawing in real life and I don't have a tablet. Neither do I know anything about human proportions. But I do know my way around Photoshop & Pixelmator. My goal is to draw people somewhat like:
Are there any good tutorials or books out there which I should check out? I don't want to mess with it until it looks good, I'd rather start bit by bit so I get good at it.
(Image from American Presidents by Peripatetic)
Without a tablet or touch device, your best bet is to use vector graphics. I mean, some pretty incredible drawings have been done using mice and trackballs, but it takes a lot of time and patience to develop the kind of control you need for drawing on such devices. If you're doing raster drawing though, you're better off just spending $40-50 to get an entry level tablet (especially since you won't have pressure sensitivity without it).
But that particular graphic looks like it was done using vector shapes/paths, and something like that can be easily created using a mouse and any graphics program that supports custom shapes/paths (e.g. Photoshop's pen tool).
As far as learning how to draw people, that's something that takes a bit of study, but there are tons of books on figure drawing and drawing human anatomy. A trip to the local library or a quick search on Amazon should turn up plenty. However, you may want to focus on cartoon-specific books, since that's the style you're shooting for, and cartoon/comic-book characters have very different and highly stylized proportions.
Assuming you have that iPad app, I would start by picking up a copy of Inkscape, Gimp, Illustrator, Photoshop, or even Fireworks, and then start copying the different presidents. Try to copy them as accurately as a possible, going through all the different presidents. And when you're done, start from George Washington again and make another set of copies. With each new set, you should get better, and you can compare the different versions to monitor your own progress.
This might seem tedious and uncreative, but this is a basic training technique that most figure-drawing and painting students have to go through. And it's especially helpful when learning how to emulate a particular style.
Lèse majesté is offering solid advice. My own recommendation on where to start would be to find local evening classes in drawing. There are several levels of skill to master: knowing how to see (not as obvious as you'd think), knowing how to draw, and knowing how to draw with a tablet.
In most countries there are the equivalent of American community colleges that offer free or very inexpensive evening or weekend courses in a wide range of subjects. One near me has everything from managing databases to making cookies, with about everything you could imagine in between. They offer various levels of art and drawing classes.
Beyond that, it's practice, practice, practice until your eyes glaze over and your wrist can't take any more pain, then do it all again the next day and the next. There is no substitute. Somewhere along the way you'll find your own preferred style, and you'll be on your way. Ken Robinson's description of Matt Groening's start as a cartoonist illustrates the point quite well, I think.
A most excellent resource would be "Drawing on the Right Side of the Brain" by Betty Edwards. I myself and a few other friends have graduated from "cartoons" to very realistic depictions of human anatomy using the techniques she promotes. Actually, our cartoons have become better as a result of her applications. Also, it can be lots of fun rather than tedium. And, you'll get to know yourself and your brain a little more intimately.
Most big box book stores will have a large(ish) discount art section and there's usually 2 or 3 anatomy/life drawing books to be had for about $10. Pick one up.
If you are really serious about pursuing it further, lots of local colleges and some larger community education centers will have life drawing courses semi-regularly where they bring in models for you to use.
Another tip is to invest in one of the little mannequin models: https://www.google.com/search?q=drawing+mannequin
