To Root For
To Cheer On, To Cheer For
する verb, transitive verb
応援 is aid and root for, but for this verb the "root for" one is going to be more on the money. You can call this to root for, to cheer on or to cheer for.
おうえんする
The reading comes from 応援. It's also just the on'yomi readings you learned.
どちらの力士を応援しているんだい？
Which sumo wrestler are you rooting for?
トーフグ社員はみんな、両足を肩はばに開いて立ちながら、コウイチを応援していた。
All Tofugu employees were cheering for Koichi, standing with their feet hip-width apart.