Zen shopping is the art of going out somewhere with a list of people in mind, but not a list of specific gifts. This works best in a place with lots of different options such as a flea market, bohemian street, or mall. You wander around and wait for something to catch your eye. As you stroll, think about the people on your list and imagine what kind of things they would like. Let your mind drift over "favorites" -- favorite color, favorite fabric, animals they think are cute, the music they listen to, etc. Don't be afraid to stop and poke through a table of goodies, but in general, keep your eyes moving -- up and down as well as side to side, because sometimes the nifty things are in odd places. Ideally you should reach a sort of meditative space in which the right gifts seem to jump out at you, look extra shiny, or otherwise grab your attention. You'll know who each one is for.
Another name for this skill is "channeling Santa Claus," particularly if you are shopping for children. There is a certain layer of reality in which wishes and desires are collected. With a little practice you can tune into that and gain an intuition for what gifts would appeal to someone. Santa Claus is just one of many holiday gift-givers such as Joulupukki or Frau Holde. Focus on whichever one comes with your tradition(s).
Talk with your friends and family about gifts. Different families have different traditions. Some people think that gift cards are tacky, while others like them. Some people think that homemade gifts show love and care, while others prefer storebought gifts. Some people appreciate intangible gifts, such as a coupon for a weekend of childcare or a tree planted in a National Forest; others don't. Ideally, find out what the people on your shopping list consider to be appropriate gifts, and aim for that. Don't feel compelled to break your budget, though. It's usually possible to find something that will suit, for a reasonable price. Think outside the box!