Depends on what the anime's like. If it's very realistic, texture and smooth motion is key.
It usually takes me 3 layers to do this, using Sony Vegas. Take a white solid, then mask out a teardrop shape- first frame, make it look like it's about to spill from the eye, then keyframe it to drop down as you like. You might want to feather the outline outward a bit, or add a blur to it, and change the motion to every 2-3 frames. This layer serves as the outline for the teardrop, as a whitish outline is typical of anime tears. Next, copy-paste the footage of your character on a layer on top of this one, and give it the same masking keyframes as the white solid. Feather it inward a little bit. If you want a touch of realism, copy-paste the white solid event from the first layer to the top layer, and feather it in until it's blurry and looks somewhat like a reflection.
Should look something like the picture here:http://www.akross.ru/pics/screens/ac2009/69-1110915022_mastamind-Debut-3.jpg
(I didn't create those^ tears, but I did on multiple occasions in that video. Just too lazy to go through it and find the scenes where I did). Good luck