This is a good thread. There are lots of ways to learn about mechanical stuff. I'll try to share how I've learned over the years.
1. Alot of stuff has been designed and developed by many smart people over the years. Study what they have done. Know that very smart people, thousands of years ago could build stuff
like this.
2. Know your basics... memorize your trigonmetric functions and conversions. Do your homework and be able to walk through a story problem. I use basic physics and trig every day, while I seldom use Calculus (but other engineers use it more).
3. Like the guys said above, be confident to take apart stuff and put it back together. I have found out that if a mechanical contraption is not working right, it can often be fixed by disassembly, cleaning, and reassembly. Work smart when disassembling things (label wires, etc.) so that re-assembly goes smoothly.
4. I get a kick out of assembling things that I buy at stores (grills, kids toys, pre-fab furniture) for my house... I follow the assembly instructions to a tee, and I am often critical of how some engineer communicated his idea through poorly written assembly instructions. Some of these instructions are good, some bad. It is good to know the difference and I am a better engineer from seeing their mistakes in communication.
5. My mom married a hog farmer when I was 14. My step father is 65 and still works every day of the week, mostly 10-12 hour days. He can fix anything on his farm from electrical work to welding, 'cause he has to. I have worked aside my step-father and I have learned to respect his hard work. He has no care for electronics, computers or all of this robot stuff - but he still respects what I do. I have learned alot from him... it takes hard work to get things done, it takes guts to try things that you may not know how to to do, and you always have to get the job done - no matter what tools or materials you have to work with.
6. (this is the most important one of all) I have learned very much from the skilled labor who I work with. My job is to design machines for Delphi-Delco production lines. I cannot fabricate parts or assemble these machines... UAW skilled labor guys do this. Some of these guys have been machining parts, wiring robots, and debugging equipment for 40 years. Most of them work hard and know how to make things work. I learn from them. It is a rare time when I release a print package that does not have a mistake in it. If these guys would want to make me look bad, then they could make minimal effort to make my design work, but if we work as a team, then they take ownership in "our" machine and they make the thing work. I look up to these guys and I have learned how many mechanical contraptions work through them. They have seen guys like me come and go often, while they are still there making machines.
So... be curious and have the confidence to learn things by using your hands, do your homework and study hard. But, most importantly, do not act like you are the smartest person in the world. Understand that not only can you learn from other experienced engineers, but also mechanics, farmers, and craftsmen.
Good luck,
Andy B.