There's some software that you can buy that will make it one-click - assuming your subjects and your green-screen are properly arranged and lit. If you don't light the subjects and background properly, then it'll be very difficult to recover it in post, even with the best software. I don't have any specific software to recommend.
The green screen must be clean, wrinkle-free, and evenly lit.
There must be enough distance from the subject to the green screen, so that the green does not reflect a color cast back onto the subject: 6 to 8 feet will be the barest minimum.
The subject must be properly lit, almost certainly requiring separate lights from the background.
Ideally, to make it believable, you'll study the drop-in background before setting up, and arrange your subject lights so that they'll mimic the lighting on your intended drop-in background: direction, size, intensity, color. If you have a neutral white three-point portrait light on your subject, and your drop-in background is a golden sunset beach, then the final composite will look fake. (note, if you're just doing this for fun/silly snapshots, and you don't care about making a "believable" composite, this isn't as important)
If you're doing it manually, a light gray background (such as white seamless paper without a background light) is almost certainly going to be easier and cleaner than a green background. There's no one-click method, though. Green and blue screens are more suited to video work.
Frizzy/flowing hair and sheer fabrics are the toughest subjects to mask. If all your subjects are bald and naked, manual masking is pretty easy.
Feet are the toughest part of a person to composite into a background, due to the perspective and shadows. Stick to half- or 3/4-length shots for easier compositing.