Witch: Any practitioner of witchcraft/magick, regardless of philosophy or religion.
Pagan: A person who believes in nature as their source for religion. Pagans are almost exclusively polytheistic (believe in more than one god). These beliefs create an underlying basis of Understanding and thinking that is the common thread about the Pagan religions. This is a VERY broad category, and can include many conflicting belief systems.
Wiccan: Created by Gerald Gardner (Also commonly referred to as Gardnerian Witchcraft). A form of paganism, mixed with other forms of the occult. Wicca has a more structured belief system, and more ground rules than many other types of Pagans.
All Wiccans are Pagans, but not all Pagans are Wiccans.
Ok, let's answer your questions more directly now...
Do you have to do anything to become a witch? Yes, technically you must practice some form of Witchcraft or Magick to be a witch.
Do you need other people to become a Pagan or Wiccan? There are two very distinct views on this. Some say yes, some say no. I say no. The first few witches became witches without anyone else (obviously), and so I don't see any reason why we can't do the same. On the other hand, if you wish to be a member of a specific Coven (group of Pagans/Wiccans), then you must go though their admission process.
There is no specific way to think/act/dress/whatever. I find that one of the most important things is to think for yourself. Figure out what you believe, and try to figure out why. If it turns out you don't agree with the Wiccans, it's no big deal. If you discover that your beliefs show you you're not even a Pagan, that's OK too. At least you'll be a better person for yourself.
As for who is right, and who is wrong... This is kind of a tricky situation. There are not many "rights" and "wrongs" in Witchcraft. Very often people will disagree about how they do things, or why. This is very important, actually, because it keeps the craft growing and changing. If you find that you disagree with another person about the Craft, then try discuss with them WHY you don't see the same way, and find out if you can learn something from each other (This also works in most other situations, come to think of it). However, if you find that you and the other person are getting agitated, just leave the subject alone. Some people see disagreement as conflict, not as a way to learn from each other.
I have found that studying the Philosophy, history, and concepts behind Paganism and Wicca are what are really most useful in the long-run. These will help you gain the best insight on how you should handle situations, and react to the world.
"To thy own self be true and it follows, like the night the day, you can't be false to any man."
~William Shakespeare
Free eBooks (Can Be Downloaded):
Paul Boyer - The Salem Witchcraft Papers Vol 3Thomas Potts - Discovery Of Witches
Judy Harrow - Exegesis On The Wiccan Rede
Georg Lomer - Seven Hermetic Letters
Max Heindel - The Rosicrucian Mysteries