Brainstorming is a very useful technique for discovering new ideas. I think it should be practiced daily by every designer. It helps to unleash creativity and to give a direction to our mind, so that it stops thinking about unnecessary things.
An idea by itself doesn't mean anything. Anyone can have the same idea; anyone can borrow ideas elsewhere. There aren't idea rights—you can only patent a concrete, unique execution of an idea. More important is what the idea means to us and how we proceed with its implementation. The latter resembles our personal understanding of the matter, which can't be reproduced.
We shouldn't evaluate ideas before the brainstorming has finished. After we have generated enough, we can sieve through them to find the best one. It's desirable to brainstorm in a group of highly divergent people, which helps to discover more unique connections between potentially worthy ideas. In the process, every person must be able to come to word and share its opinion. It's important to generate as much ideas as possible in a predefined time interval, because the quantity and the depth of thought will determine the quality of the ideas.
Sketching ideas on paper is common, but you can also use tools like FreeMind, which help you organize your thoughts visually. If you want to innovate, it becomes increasingly important to have both bright ideas and efficient implementation.