Practice makes perfect
I think the key to training your listening skills really is regular practice. I'm not referring to just exam practice, which can get tedious, but using real authentic sources. This can be podcasts, series or youtube videos. Just find what interests you and away you go!
In my classes I tend to use real sources like this, even turning them into exam-style questions. The problem with official exams is that the listenings are not real: they are scripted. A real listening should be interesting and engage you in the topic. After all, if you are bored, are you really going to be paying full attention?
For this reason, I'd suggest finding something that you're really into. There are plenty of youtubers these days talking about a range of topics including fashion, cooking and travel. There really is something for every interest!
For high levels, I'd also really recommend Guardian Long Reads, where you can find podcasts to accompany the articles so listening and reading practice - the best of both worlds! Tedtalks also have transcripts for their videos that are available online.
Reading after you listen really is a good way of increasing your range of vocabulary. Perhaps you could print the article or transcript out and highlight any new language to study. You can always listen again once you are more familiar with it.
Of course, if you have an upcoming exam, training for the exam-style questions is very important. Your English teacher should be able to give you tips on how to effectively do the listening exam. My best tip for you is the importance of paraphrasing.
Paraphrasing
Paraphrasing is expressing something in a different way. In your exam the written questions use different vocabulary to the audio. Therefore, you should be prepared to listen out for paraphrases.
Paraphrases may include phrasal verbs and expressions to really test your vocabulary knowledge. The more of these you learn, the more chance you will have of understanding the listening exam.
Here are some examples of expressionsused in CAE listening exams:
be expensive --- cost an arm and a leg
save money --- tighten your belt
be annoying --- get on someone's nerves
a rural location --- out in the sticks/ off the beaten track
have an argurment (with someone) ---- have words (with someone)
reveal a secret ---- let the cat out of the bag
enjoy (something) --- get a kick out of (something)
have a natural talent (for something) --- have a gift (for something)