I just want to look at problems that I encounter a little differently. Trying to do everything the conventional way isn't always the best solution.
Some of it has to do with how you're wired, but imo, people can practice almost anything and get much better at it. And it sounds like you're just looking for some brainstorming practice. (I think it often gets a bad rap because people have been shown bad ways to do it or just feel stupid trying.) Just start a daily practice.
For example, every sunday, write down 7 problems you want solutions to and assign them to days (assign your problems ahead of time so you're less likely to skip). Set aside a couple of hours per day at first. You'll get much faster soon, but it's a new way of making your brain work, and your brain will resist like crazy. Then sit down with no distractions/interruptions (very important for getting into the new mental space), and write down (ideally with a pen/paper so the computer isn't a potential distraction) 100 different ways to solve the problem. Yes 100. They don't all have to be good, they don't all have to make sense even. This is the non-filtering point that people seem to fuck up with brainstorming. It's almost like stream of consciousness writing.
That's really the end of the exercise, but if it's an actual problem that you need to solve or if you just need to prove to yourself that this is useful or that you're getting better, the next step is to turn on the filter. A big part of the habit is just learning how to turn your filters off. People (especially logical, rational people) are so critical of everything that anything outside the box gets rejected by your built in sanity heuristics. However, you really need filters off for idea generation. You brain can let go a little more easily if you tell it that the filters can come back once you go into evaluation mode. Write drunk, edit sober, so to speak.
For evaluation mode, start by tossing out the first 20. That will feel terrible, but the first few are the answers that come the easiest. That means they're the first few answers that everyone will have. If you had 20 people do this for the same problem, their first 10-20 answers would have massive overlap. Not outside the box at all. This is basically the chunk where you're cleaning the goop out of your brain. Those answers were already there. You didn't have to create them. You just 'knew' them from your previous experience. Great for a quick solution. NOT great for a creative solution.
After that, quickly scratch out the nonsensical ones (and there will be a lot of those, especially at first). Then give the ones that are left a little bit of thought individually, but trying to keep a very open mind. For each one, try thinking, "if I absolutely HAD to make this solution work, how would I do that? what would the result look like?" You can't take too much time here or you'll get frustrated and quit, but the point is to give each idea some real thought so you don't discard something that might have been a great idea if you'd just dug into it a little.
After another round or two of elimination based on situation or practicality, you can probably dig out 3-5 interesting and workable solutions that you can really dig into, discuss with colleagues, etc, and they'll almost certainly be better than anything in your top 20 (if that's not true, then you were probably dealing with a problem that was already solved instead of doing the actual problem solving yourself).
One warning, if you're doing this in relation to work: DO NOT try to do this as a group. It will be chaos, and everyone will hate you. The best way to do this with a group is to give everyone the instructions, have them do it on their own, and then they can bring their 3, filtered, polished answers back to the group. (Even if you could make them, it's impossible for most people to really turn off their filters in front of a group.)
