The popularity of radio controlled model airplanes has exploded in recent years. You can find RC model airplanes for sale in most toy and sporting goods stores. There is no shortage of complete packages on the market that sell for less than $50, though I do not necessarily recommend these bottom drawer systems.
The process for learning to fly model helicopters properly is very similar to what I describe here, but I will be focusing on airplanes.
Local Hobby Store
Before you do anything else, find yourself a local hobby store. They specialize in helping out beginners such as yourself. They don't bite, and they will respect your budget by not steering you to equipment you cannot afford. Their prices are very competitive, and the advice is well worth any small price premium. Just make sure you are speaking with somebody that knows about model airplanes. Hobby stores carry products for many different hobbies such as RC cars and model rockets. If they have a reasonable selection of model airplanes in stock, there is guaranteed to be somebody on staff that understands them.
There is an important side benefit to visiting a local hobby store first. They are very likely to have an RC flight simulator running for you to play with. Try it out! Expect to crash a lot at this early stage, but you will get enough of a taste of RC flying to see how you like it.
Local Model Airplane Club
Next, find yourself a local model airplane club. Ask at the hobby store. They should know. Clubs are invaluable sources of information. If you go to their flying field you will get to see first hand the different types of model airplanes that the club members like to fly.
When you join the club you will probably be asked to also join a national model airplane association. In the United States, this organization is called the Academy of Model Aeronautics, commonly referred to as the AMA. With your membership you normally get a nice magazine. When the first issue arrives, read it. You will learn a lot.
In the United States a very important benefit from joining the AMA is accident insurance. Most clubs won't let you fly from their field without being an AMA member because of this. Be smart. Join your national model airplane association. Joining the club and national organization will set you back from $50 to $100.
Clubs always have assigned flight instructors ready, willing, and able to help you out. Make use of them! As long as you are polite and eager to learn, they will be very happy to teach you the ropes.
A lot of clubs have trainer airplanes for members to use with an instructor. They also have trainer cables to hook up two RC controllers. Sometimes this is called a buddy box system. Then the instructor can easily take over from you in case you get in trouble. This is a tried and true way to learn to fly RC.
RC Flight Simulator
A great alternative to learning to fly with an instructor at a club is by using an RC flight simulator. If you don't have an instructor with a trainer airplane and trainer cable, it makes absolutely no sense to try and teach yourself how to fly using a physical airplane. The simulators are a lot of fun and very realistic. If you can control the model airplane in the computer, you can control a real one.
Don't confuse a PC flight simulator with an RC flight simulator. PC flight simulators, like Microsoft Flight Simulator and X-Plane, are primarily for simulating full-size airplanes. You want a product that comes with an RC controller and is optimized for teaching you how to fly radio controlled model airplanes.
To get the most value out of these RC simulators, you have to fly the simulated model airplanes as if they were real model airplanes. Always begin and end each flight with a proper take off and landing. The biggest mistake that I see people making is to act like they are playing a video game. They do stupid things while they fly and every flight ends in a crash. All they are doing is learning bad habits.
Great Planes Real Flight Basic
There are two RC flight simulators on the market that I recommend. The first is called Real Flight Basic from Great Planes. It only costs about $100 and it comes with everything you need. The package contains a decent RC controller and enough simulated airplanes (about 50) and flying fields to keep you entertained for a long time.
The only other RC flight simulator that I can endorse is called Phoenix. If you own a Mac, this is your only choice. What I recommend is that you purchase the version with the included Spektrum DX5e RC controller. You see, RC flight simulators normally come bundled with RC controllers that are only good for using with simulators. That's fine, but you would be better off being able to use a real RC controller with the simulator. Then the controller would have the same feel when you fly the simulator as when you fly a real model airplane. You can also save some cash by not having to buy two separate controllers.
The version of Phoenix with the DX5e controller does exactly that. It includes a real five channel controller. At $175 it is a bit more expensive than Real Flight Basic, but it includes 150 simulated model airplanes and the controller. These added features make it a much better deal, in my opinion.
The choice of a first RC model airplane needs to be made carefully. The vast majority of airplanes on the market would not make a good choice. Most are too hard to fly when you are just starting out. The rest have either poor performance or poor durability. Many times both! Making the wrong choice can be a very frustrating experience.
The kits I recommend below can be purchased with or without an RC controller. If you buy them with an included controller, keep in mind that it will most likely be a very barebones unit. You will want to upgrade to a better controller soon, probably for your second airplane. That is why the Phoenix simulator bundle with the DX5e controller is a good deal.
Also keep in mind that the controller needs to be matched up to the radio signal receiver that goes inside the airplane. If you already have a controller and the airplane you want to buy comes with a receiver pre-installed, do not assume that they will be compatible with each other. Ask at the hobby store or club first.
Multiplex Easy Star
My first recommendation for a beginner's airplane has to be the Multiplex Easy Star. A ready to fly bundle with an included RC controller goes for about $200. This powered glider flies slowly, is very stable, and is very durable. It is easy to see in the air and can be flown from any reasonably sized park. Yes, this is pretty much the perfect trainer.
Even better, both RC flight simulators I recommend include the Easy Star in their list of simulated airplanes. You cannot go wrong with that!
Parkzone Night Vapor
This one is a personal favorite of mine. I won a Vapor at a club raffle a couple of years back. I probably have over a hundred flights on mine. Weighing about half an ounce (16 g), it can only be flown outside on completely calm mornings. Don't try and learn to fly it in your living room. It won't be big enough.
Ask at the club about indoor flying. Around here, we have indoor flying on Friday nights at least a couple of times a month. If it weren't for the requirement to find an indoor flying location, this would be my first choice. With a bundled controller, it only goes for about $120. It is very durable and flies great.
So how long does it take to learn to fly RC? That is like asking how long it takes to lose five pounds (2 kg). It totally depends on you and how much effort you put into it. I would say that with reasonable diligence, you can be flying your very own RC model airplane in a month or so.