Difficulty: Moderately Easy
Step1
Check out their art desk. Look for supplies they appear to be running low on, what they use most and what looks hardly used.
Step2
Take a look at their video collection. Most animators don't just create animations; they watch them as well. Maybe you can buy a video collection of their favorites, or fill in a gap in an existing collection.
Step3
Look for memorabilia. If they have a favorite animation, look for product toys and other related merchandise.
Step4
Listen when they talk about their animation needs. If you quiz them, they may catch on to the gift, which will ruin it if it's a surprise. If you listen, though, they may mention something they want but can't afford, or something difficult-to-find that you can track down for them.
Step5
Listen, too, when they talk about their problems. If they have issues with drawing anime style, get them an instruction book on that type of animation. If they bemoan their walk cycles, get them a book on how to animate fluid walk and run cycles. You can gift them not only with material things but also with the means to improve their skills.
Product image taken from Texas Art Supply (texasart.com)