For those brave enough to step out into the world dressed as a blue haired sword wielding lord of death, or some other noticeable and strange costume, it can be scary to try and take photos or even just walk around in costume with so many people with their eyes cast towards you. But don't be scared! As long as you remain polite and well behaved, people are more curious than disturbed.
You see, if you don't cause trouble and appear approachable people generally wont cause trouble for you and will probably approach you and ask "What are you guys doing?" Generally, people already have an idea that you are taking photos because of the presence of a photographer, but they're still curious about that gorgeous person with the crazy costume. Should you be approached, be polite and don't lie! An answer something along the lines of "a costume photoshoot" should do the trick. Should they ask what you are dressed as, it's always safe to say a general description of your character. For example, if I were dressed as Ezio from Assassin's Creed I would answer "a character from a video game" or "an assassin". Simple but polite answers will interest this person, but answer enough that they aren't confused, and most of all wont annoy or aggravate them.
Dealing with children can get a bit trickier because they love to ask more and more questions and in some cases they want to play or interact with you. It's best in the latter case to avoid playing with kids. While it might be fun, it might not be appreciated by said child's parent(s). When answering who you are dressed as, a bit more simplification might be necessary, as a child might not understand what an assassin actually is. Generally going with descriptive words like warrior, hero, knight, princess, ect should do the trick. If a child asks you if you're a real prince/princess/knight/ect it's up to you how to respond. While I'm hesitant to overexcite a kid, I've found answering with something like "Yes. I am a princess from a very far away land" not only put a smile on that child's face, but answer their question.
But the single most important thing about cosplaying in public is to ALWAYS be polite and obey the law. It makes a terrible name for cosplayers if you go around stealing, vandalizing, harassing, or disturbing the public peace. Not only do you bother and hurt other people, you get in trouble and so does the rest of the cosplay community. If you're in a big group, it's advisable that you stay away from crowded public places like malls, but places like parks are still a-okay. Never be rude to people. It makes a bad name for you and cosplayers. It doesn't hurt to be polite because as long as you are polite people wont bother you, the police wont bother you, and you can have a fun time at your photoshoot and/or meet-up.
Remember: While you may be scared of the public while cosplaying, the public is mostly interested... so long as you aren't causing trouble.
(Of course, there are always bad apples and people who will harass cosplayers. Generally, these people are in places you probably shouldn't be for taking photos. People in parks and public places tend to be either not interested or happily intrigued. But, should you be worried about harassment from the public, always go out with a group of at least three people. If something happens, call the police, be honest about what you were doing (doing a photoshoot, really they will understand. Cosplay isn't something to be embarrassed about) and always make sure that you stay away from bad areas of town or densely populated places where you and your cosplay friends will only be in the way.)