Teach yourself to cook
Everyone knows that cooking is cheaper and healthier than eating out. It's also better (i.e. more to your taste) than eating out, and easier than eating out (no driving, parking, standing in line, making reservations, waiting to be seated, dealing with hostesses, waiters, and busboys). Besides all that, I'm going to argue below that--even with shopping and cleaning up--it can also be quicker than eating out.
If you currently eat all your meals out (for example, you live in a dorm with meal plan), you probably can't save time by learning to cook--because going shopping for groceries is another whole task that you'd have to add to your schedule. But if you're already maintaining a kitchen but don't use it much, then the extra time to buy all your food (instead of just a fraction of it) is quite small.
Cooking, of course, takes time, as does cleaning up. But then, going to restaurants takes time as well. Fast food joints that cook ahead may serve your food quite quickly--but that's never going to be better or healthier than your own cooking, and even with a dollar menu it's not likely to be cheaper. It may be easier--if you think driving to the fast food joint and then standing in line is easy.
On the other hand, cooking lends itself to any number of simple efficiencies that restaurant eating doesn't, simply because you're in control of things like the number of servings you make. You can save a lot of time by cooking enough that you have dinner today and lunch tomorrow, without the complexity and waste of restaurant-sized portions that may provide leftovers, but rarely in the right amounts or right proportions.
Like with anything else, the way to learn to cook is to do some cooking.
With a few exceptions--confections and pastries, mostly--cooking is actually really easy. Anyone can learn to boil rice, bake a chicken, or grill a steak. Certainly anyone can learn to make a salad.
If you know even a little bit about cooking--what a saucepan is, what sauteing is--then you can start with recipes.
If you don't cook at all, try to get someone to show you how to cook--your mom, your wife (or husband, boyfriend, or girlfriend), or even a friend at work who brings in leftovers for lunch. If you can't manage that, there are plenty of cooking DVDs and internet sites with videos where you can learn the basics. There are also plenty of cookbooks that cover the basics (Joy of Cooking is the classic, but there are others--any number of cookbooks aimed at newlyweds, for example).
Once you know the basics, start by learning to fix two or three things that you particularly like to eat. Once you have those down, learn how to make one show-offy thing that you can use to impress a date, spouse, or the in-laws (or just to treat yourself, when you might otherwise be inclined to go out to eat).
So, how can cooking for yourself save time? As I suggested above, mainly through efficiency--cook enough that you have leftovers and your next meal takes almost no time to prepare.
There are people doing extreme versions of this--cooking a whole month ahead, for example--which is fine if that's what you want to do, but not really necessary.
It also gives you extra control--you can decide when to fix something quick and when you've got time to spend preparing a special meal. (Ever gone into a restaurant for a quick bite that ended up taking two hours because the waitress was incompetent and the kitchen was unaccountably slow? I have.)
Of course, to save time you have to make that a priority right from the start. There are dishes that take large amounts of prep time--but since you're in control, you just don't cook those when you're pinched for time. There are lots of things that can be fixed quickly--and other things that at least don't require much time in the kitchen. (Crock-pot meals are the classic example of the latter. Personally, I don't have a crock pot, preferring instead to use a pressure cooker.) (See also: The 5 Best Pressure Cookers)
But you don't need to actually cook in some special way or follow some special process to save time--just choose things that can be prepared quickly: salads, sandwiches, stir-fry, pasta, roasted vegetables, poached seafood, grilled meats, etc. Breakfast dishes are typically quick to cook, and plenty of them (omelets, for example) are easily adapted for dinners.
Even when you optimize for time, cooking and then cleaning up takes some time--but so does going to a restaurant, ordering, and waiting for your food to arrive. Of course, cooking requires grocery shopping, but if you're already shopping, the extra time it takes to buy enough to fix most of your meals isn't much of an increase (unless all you're doing now is keeping your fridge stocked with beer and soda)--just be focused and efficient. Again, it's possible to take this to extremes as well--sort your shopping list into the order you'll find things in the store, for example--but that's not necessary either.
In fact, though, simple efficiencies like keeping staples on hand mean that you'll be able to shop less often, because you won't have to make special trips to the store due to running out of something. (Stocking up on cheap stuff also provides a huge financial return.)
Having it all
The core win of knowing how to cook is that it expands the range of what's possible. Just because you've learned to cook doesn't mean you can't eat a restaurant meal when you want to; it just means that you don't have to. Instead, you have a bunch of options that are all cheaper and mostly healthier and better.
For example, I rather like french dip sandwiches. I can get one at a good local restaurant; around here a french dip meal might run $15 a person plus tip. Or I can go for cheaper options. At a chain restaurant I might be able to get out for $8 plus tip (except that I'd probably buy a soda or a beer, adding a few dollars to the tab). The last time I got a french dip at a fast-food joint, I think I spent a little over $7 (which included fries and a soda that I'd probably have been better off without).
At the deli counter at the grocery store, roast beef tends to run about $9 a pound. I sometimes buy a package of sandwich rolls, and then get just enough roast beef to make one sandwch--for a total of about $3.50 (mustard plus a bouillon cube and some hot water for the dip will add a few cents to the cost). The sandwich rolls, though, come in packages of four or six, so once I've made my french dip I can make several more really cheap sandwiches (just the cost of the deli meat) over the next several days. (And they can be something different--chicken, turkey, and ham are all usually cheaper than roast beef.)
Which brings us, finally, to cooking. For not much more than the cost of one serving of deli meat, you can get a big hunk of raw meat--if you buy a cheap cut that's been marked down because it's approaching its sell-by date. Cook that in the pressure cooker (or roast it, if you happen to find a good deal on a nice cut). For example, last week my wife found a shoulder roast on sale for about $5. That plus $2 for the sandwich rolls and maybe 50¢ worth of onion and garlic made six sandwiches, so about $1.25 per sandwich.
I spent about half an hour cooking the meat: While I cut up the onion and a couple cloves of garlic, I browned each side of the meat in the pressure cooker pot over medium heat. Then I added two cups of water, put the lid on, brought it up to high pressure, and let it cook for 20 minutes.
I also spent a few minutes cutting the meat into thin slices for sandwiches and a few minutes more building the sandwiches--but I've waited longer than that to get served at a fast-food joint.
I don't think anybody disputes that cooking is cheaper and healthier than eating out. It's only better, I suppose, if you're a good cook--but you don't have to be a great chef to fix stuff exactly the way you like it, you just need to practice a bit. Is it actually faster than eating out? Well, it can be--if you stick to stuff that's quick to fix, or if you go to some effort to be very efficient, or (especially) if your basis for comparison is a nice restaurant rather than a fast-food joint.
I think it adds up to plenty of reasons to teach yourself how to cook.