How to suceed in mathematical olympiads and competitions?

This question may be slightly off-topic but it still relates to Maths so I hope that it does not get taken off.

I am a student who is 16 years old, is generally good in Maths and enjoys it and I really don't have a problem with it at all. Calculus, Geometry, anything you can name, but I have a slight problem in doing well in mathematical competitions where they ask problem solving questions and questions that require you to think out of the box (Similar to other questions I've posted on my account). I really struggle to answer half of the questions in the Maths Olympiads but I have no problem with routine-type questions such as solving equations, simplifying, calculations, etc. I usually get good grades for Maths so I always wonder why I struggle with these questions.

I have a Math Olympiad coming up soon and I was wondering how could I do well in it and if there are any tips and guidelines I should follow to succeed in these Olympiads? I've been practicing by doing past papers but it doesn't seem to help me much. Any advice will be greatly appreciated as I really want to do well in the Maths Olympiad.

It's largely a matter of intensive practice in solving the right problems. You would want to attack simpler problems first - a good place to start is the AMC and 1938-1960 Putnam problems. Then you can move on to AIME or similar level problems, and finally olympiad problems.

Problem solving books, like those by AoPS or by Zeitz are also good.