Before I start pontificating, a disclaimer... My experience is necessarily US-centrc as that's where I live and work. Over the years these methods have worked equally well for me in large cities with jackboot-style authorities (LA, New York, etc.), as well as smaller cities (potentially where the authorities have less oversight and more willingness to shoot first and ask questions later). If you live outside the US, YMMV.
Question: Is there a common phrase or such, that photographers generally use in these situations? Something I could print up on a card with a name, phone number, and email address.
tl;dr: There's not really some 'common' phrase (despite rumors to the contrary, a blank card with the phrase 'Tubal Cain' will not instantly make any authority figure your b*tch, or for that matter get your court case dismissed!). It's more about confidence and positive interaction with people that allow you to shift yourself from the 'sketchy' column to the 'trusted' one.
Over the years I've found that 'dealing with the public' and 'dealing with the authorities' are sometimes two different challenges... However, often the 'tactics' are similar and dealing with both groups starts from the same place: confidence.
In dealing with the public I 'assume the right' and only ask for additional permission and/or explain myself if I'm first approached. I find that the more confident I am (not arrogant, combative, or argumentative... again, just assuming the right) the less often I get approached. Most of the actual 'horror stories' (as opposed to the often breathless and 'over-hyped' 'big-fish stories' that some photographers like to share on the interwebs or when drinking with their photographer buddies) actually occur because a photographer didn't have polite confidence, and/or they didn't handle the interaction in a positive manner.
If I am approached, I have a 'patter' that I use which goes something like this:
"Hi there, my name is Jay Lance from Jay Lance Photography. I'm a professional photographer on assignment."
[As I'm saying this I hand them my business card... There's nothing 'special' on my card aside from the fact that it is professional looking and contains my contact information. Essentially my opening 'move' is to give them a bunch of identifying information without them having to ask or try to pry it out of me... I've told them my full name, my businesses name, and given them my contact information... All information I give willingly with the intention of showing I have nothing to hide, and all information that matches what's on the business card... The sole purpose of doing this is to begin building trust. I don't generally elaborate that the 'assignment' I'm on is usually assigned by... well... me.]
At this point I strike up a light conversation where I'm trying to do most of the question asking and listening...
['What's your name?' 'Lived here long?' 'How about this weather we're having?' It doesn't really matter as long as I do the asking and really take an interest in the answer(s). The point is rapport building and showing that I'm 'harmless' without ever actually having to say that I am or explain myself (attempting to explain can sound like excuse-making and trigger some people's inner-alarm regardless of the intention).]
After a few innocuous questions I generally finish the 'conversation' this way:
"Well [name], it's been really great meeting you, but I gotta get back to it. Feel free to give me a call at the office [referring to the card I gave them] if there's anything else I can do for you..."
[Politely trail off at the end of this... Resist the urge to explain or justify yourself further and clam up without being dismissive. If the only reason you were approached in the first place was so that the person could make sure you weren't 'sketchy,' then the business card + rapport building conversation should have alleviated their concerns. Most of the time the 'social cue' of 'you're interrupting me while I'm working' that you've just put out there will cause whoever has approached you to dismiss themselves, apologize for bothering you, or something similar.]
After all this if they do have a specific question ('what are you doing?') or request ('please don't take pictures of my house') I answer directly, or comply with any reasonable request. Remember that because I actually don't have anything to hide answering direct questions is no big deal! Sure, technically I have the right to take whatever pictures I want, but c'mon, is it that important to escalate to confrontation over the picture(s) you want to take (or took)? Unless it actually is that important (Holy sht, a UFO just landed in your front yard and I'm the only one with a camera!) generally the only thing to be gained by not complying with the person's request or acting like an ashole is to create argument and potentially instigate a chat with the authorities. Which brings me to...
While much of the above still applies to dealing with the authorities (assume the right, business card up front, polite 'light conversation' which tells someone you're not a threat, etc.) it's important to remember that an authority figure generally has training and extensive experience in 'dealing with the public,' and is far less likely to be impressed by you, your camera, and your patter.
This is the point where some well-meaning photographers are getting themselves into trouble.... Remember that 'knowing your rights' and 'explaining your rights to a cop' are two different things and unless your idea of a good time is spending time in the back of a squad car while a cop figures out what to do with you... Seriously, knowing how you plan to approach this conversation is something to think about before you actually have it!
Having said that... There is an 'almost magic bullet' that you should always have in your back pocket (figuratively- you should actually have this clipped to your camera bag or around your neck) for when you are approached by an authority figure... Something that can strike fear into the heart of any good public servant, rent-a-cop, building manager, or administrator: the power of the press. That's right... I'm talking about every photographers secret weapon: the press pass.
There is nothing like a prominently displayed press pass to convey the unspoken message 'I know what my rights are and I can make serious public embarrassment and possibly lawsuit trouble for you and your organization if you step on them!' without ever being confrontational or even having to say that out loud...
Now there was a time when press passes were a tightly regulated commodity, but these days its possible for any 'average Joe' with a bit of money to get their hands on an actual, legitimate press pass from a real press organization and the credentials that come with it for about the price of a meal for two at a nice restaurant.
The press pass adds legitimacy to your patter, and also subtly lets the authority figure know that you probably know more than the average citizen so they should tread carefully. Now don't get me wrong, I'm in no way advocating that you take an adversarial stance with anyone (unless it is your goal to get arrested and test out the bounds of freedom of the press within the court system). What the press pass potentially does is tells the authority figure that you're 'legit' without you having to use a lot of words (which often only serve to make you sound guilty of something... Even if you're not).
For me the desired outcome is that I shift myself in the authority figure's mind from the 'unknown' column to the 'trusted' column as rapidly as possible. The outcome of the conversation may still be that I don't get what I want, but if I'm asked to leave politely as opposed to being forced to leave in handcuffs, or being treated less-than politely in some way, then the badge has done its job. That's the worst case scenario. In practicality I've had many occasions where flashing the press pass flipped me from 'suspicious' to 'trusted' so fast that I've actually had authority figures offer to help run interference, or to escort me to places that 'the general public' is not allowed to be.
Now I do have to say this... don't lie. Having a press pass doesn't mean you work for the New York Times (unless you do), but most of the time that just doesn't matter. Especially in this day and age where there are more media sources than ever and many are farming out their reporting/photography, being 'freelance' isn't a badge of shame. If asked I proudly (remember that whole confidence thing) tell them that I'm a freelance photographer, and if pressed further I am happy to let people know that I can't talk further about the specifics of the assignment that I'm on. The bottom line is this: professional, polite, and confident will often get you a surprisingly long way a lot of the time.
Finally, depending on where you live it may be possible to take things one step farther and actually become an unpaid freelance photographer for a local newspaper or other media outlet (a 'stringer' in the industry parlance). The photo editor at my local 'real' newspaper and at one of the bigger local free papers will acknowledge my affiliation with them simply because I provide a few shots for their publications every year. All I had to do was ask...
So where to get these press passes? If you can't get one via your local media outlet (you often won't be able to unless you're a paid 'staff' photographer, but it never hurts to ask) There are a variety of organizations that offer them, but two of the more 'legit' sources (they have photographer registries that someone could look you up in, in other words) are:
For a yearly fee both will register you in their database and give you press passes. In my experience the NPPA is more 'legit' than the US Press Association, although I've never had anyone ever question my credentials or 'have to look me up' to verify them, so in reality it probably doesn't matter that much which you go with... You do get a monthly magazine with the NPPA dues, though. :-)