Before Battles
First thing you should do is know your Yo-kai. Go to their pages and look at their stats. Look at what is lacking and what is stronger, as well as their attitude and how much they are prone to loaf. It's better to know it as soon as you get them so you can use the according book to change their attitudes and raise specifics stats. There are already info on it around this sub!
Then go to their moves page and get to know it too. Most people don't read it and they don't really know how much damage their Yo-kai can do and what are the elements their moves are. Some Yo-kai can have two different moves with different elements, that's something you should check when changing attitudes as well.
Use those books that level-up specific moves. The higher the level, the bigger the damage.
Know the skills of Your yo-kai and make use of that. Some yo-kai will affect their friends and some their foes. It's better to know what are your skills when placing them on the wheel as well so you can choose which you want in battle by turning it
Make better use of the items. There are special items like the Vampiric Fangs in YW 1 and the Revenge Soul in YW 2 that will heal your Yo-kai a bit for every physical hit he does. Don't give it to a Yo-kai that does elemental damage...
Make use of the unities. They are great. Bonuses are always great. You should try having more than one unity at the time so you can spin the wheel and get a new bonus.