"making an effort" means that you are trying hard to achieve your goal whereas, "taking an effort" means the task you are carrying out is making you work hard. For example, "John is making an effort to lose weight by going to the gym regularly." whereas "It is taking a lot of effort on John's part to lose weight". The first use puts the subject as the person using the effort to achieve whereas the second makes the effort the subject. Hope this makes sense for you!