Seeing patterns means two things. The more mundane thing it means is building a bunch of connections between different concepts, either pairwise or by lumping things into categories. The less mundane thing it means is to see gradients and analogies among multiple things, and to be able to do it on the fly.

The mundane thing is (sensibly) easier to train. You have to establish these connections in the first place, for example by reading "how things work" books, or just by being curious, or by talking with other people about categories. And then you have to practice, which I recommend doing by playing a game. You take a thing, and then you take turns (assume you play with other people) naming other things this thing could be, if you squint your eyes a bit. For example, a tube of lipstick could be a tiny red mirror with a handle, or it could be the latest thing in paintball bullets, or it could be a melted eraser, or it could be a portable snack, or it could be a dotted-line-drawer for apprentice surgeons, or... the beginning of the game is easy, but the trick is knowing how many times to just keep going even after you think you're done (about 2, in my experience). This is a really good game for car rides. For example that thing with the tarp on top of the other guy's car could have been a smuggled alligator, or it could have been a heavy-duty tent, or a blue whale condom, or a defective parachute, or an inflatable robot, etc.