how do you acquire new techniques?

when you Adventure and defeat monsters, your monsters gain Anima. In the menu, there's an icon called Anima, where you can pay anima to aquire new moves.
Note some moves can't be learned right away - they might need another weaker move to be learned first.

YOu buy them using AP.

Go to the menu using the square button when not in show or meeting, an chose the option anima... (the Icon with the heart and the + sign.

you can also use the trials from the guild to gain anima.

Doing adventures is a better source as you have more battles to work with. Most of the high end techs will be over 2k in needed anima to get but its easily achieveable.

well, it depends...i raise my monster having trials every wk....they gained around 70 ap per wk. i dun think it increase any tiredness and does not waste 1 wk going into adventure. mayb i am wrong...still new to game

The adventures will probably give you more anima. And three monsters recieve anima. They make even more if they KO'd the most strays.