This is not to say that people should not learn karate at home, actually I believe learning karate at home should be encouraged.
The karate warm up and stretch is an extremely important and sometimes over looked are of karate practice. The warm up and stretch should be thorough. Not only is this great exercise and healthy, it will also greatly reduce the risk of injury.
The basic karate moves for beginners, consist of a few punches, kicks, blocks, strikes and stances. These karate techniques can be practiced at home with the right training materials. Having some great karate books, DVD’s or online resource is essential.
The karate kata (forms), is a great part of karatedo (the way of the empty hand), kata is definitely my favourite part of karatedo. There are many kata, ranging from the very basic, like kihon kata (taikyoku shodan), which only contains one stance, zenkutsu dachi (front stance) and two different karate moves, oizuki (stepping punch) and gedanbarai (downward block), right up to the very advanced, like unsu, which has many different stances and techniques, including jumps, spins and kicks from the floor. All the kata take a lot of work, so research and practice is essential.
When learning karate at home, the stumbling blocks arise on the next part of karatedo practice, which is the kumite (sparring). I really do not recommend sparring at home without the eyes of an expert sensei (teacher) watching you. It is at this point I recommend looking for a local karate class and there are some very good karatedo dojo (schools) out there. Just make sure you visit a few before committing to one, find the karate dojo and sensei that suits your character, because they vary tremendously. I know there are people out there who have no interest in the sparring and are only concerned with the health aspect associated with karate training. So maybe these people are in a better position to practice karate at home, as long as you understand, without kumite (sparring), your karate will be incomplete and if you are looking for self defense, you must practice kumite. Ossu!