I have been using masks to cut out a person and put them into a new photo. The issue is they look "cut out". What is the best way to soften those edges and is there a step by step tutorial on how to make the new image blend in better with the background?
You could add a bit of Feather to your mask.
*If your mask is already created, CTRL-click it in the Layers. Then Select menu->Feather. Set an amount, hit Enter. Shift+Backspace, select White. You'll need to experiment with the feather amount to get what you want.
If you create your masks by painting them, use a softer brush for the contours.
If you drag your layer from the original image (with the mask) to your new image, it will be easier to fine tune everything since you will have instant feedback.