Academic schools will have students with high levels of academic ability, but they are mostly exam-oriented which can mean that communication is not always considered the most important aspect of English education, as it is not tested. On the other hand, the students are very bright and are often interested in English.
Every high school will have official textbooks, but many teachers will be open to the idea of supplementing the text with materials you can make or find on your own. For example, you could use the textbook as homework and then design some kind of in-class activity to supplement or extend what was being taught in the lesson in a more communicative way. High school ALTs usually have more freedom with regards to what and how they teach. Some schools will allow ALTs to plan and prepare everything for themselves, so be prepared to do the majority of lesson planning.
High school students are not usually as active and attentive as junior high school students are. It can sometimes be difficult to encourage participation in class. Group work or pair work activities are a good way of getting around this problem. Using a hanko/stamp system may also be effective in motivating class participation. Don’t assume that because students are unwilling to give you the answer, it means that they don’t understand. Many students have good listening comprehension.
More than good ideas, more than experience, more than anything, you will simply need a huge amount of patience, flexibility, and energy. As an ALT you have to shoot lightning bolts of energy out of your pores because the second you let your energy drop, the class goes with you.