I have shot street and documentary photography for many years. Although, I have slowed down a bit on the street photography because of mobility issues as I get older. While I am a huge fan of Gilden's work, I could never shoot like that. It is just not in my nature to be as confrontational as he is sometimes. However, his documentary stuff is outstanding.
I carry business cards with me that states I am a documentary photographer. The cards have my name and email address on them. I have literally given away hundreds of these cards over the years. If I take a photo in public of someone and I see they have seen me do it and they act annoyed or are just puzzled, I walk right up to them smiling, and hand them a card and tell them exactly what I am doing. I always tell them if they want a copy of the photo to email me and I will send them one. Every now and then, people ask that I delete the photos immediately, which I do.
This has worked well for me. The moments where people are genuinely interested in what I am doing (and many are flattered that I find them interesting enough to take their picture), far outweigh those who got upset over me taking a picture of them. Being kind, being cordial, and really being interested in folks goes a long way in life in everything we do.
Here is a recent example that happened less than a week ago. I started a new project where I am documenting all the historic old buildings and homes in my small town. I was standing outside a beautiful home built back in the 1800s, shooting different angles of it. A nice lady came out and asked me what I was doing. I smiled, walked right up to her, handed her a card, and explained my project. We had a nice chat about the history of her house and I showed her some of the photos I had just taken.. Two days later, I received an email from her asking for a copy of the photo. I gladly sent her one by email and she replied, thanking me for the lovely photo of her home.
I know this approach may not work for everyone, but it has worked for me for many years now.