My son is eleven years old, and I struggle with how to teach / empower him to apply himself. For example, when he first started playing the trumpet, he didn't want to practice, but I explained that if he practiced, he would get better. His school's music teacher required we sign off that he practices 80 minutes a week, which he did (unwillingly, but he did it), and over time his trumpet playing was great. He hated practicing, and when the school year ended, he decided to turn his rented trumpet back in and stop playing. He says he's not good at anything...when I tell him if he works hard and applies himself, he will get good, he seems to not understand this. It seems like he doesn't want to work hard, and I don't know how to get him to see that if he invests the time and effort, it will pay off. Any ideas?
You seem to have needed to do a lot of cajoling to get him to practice! (I infer this from "unwillingly, but he did it".) Even with all that practice and eventual improvement, he wasn't self-starting the action: even though he did the work, he isn't making the mental connection. You're hoping he sees "my work = my success", but he's probably perceiving "my parents push me = I won't succeed without them pushing".
A notion that may be relevant is praising effort over intelligence. In the case of the trumpet, did you praise the time spent practicing or the resulting improvement? Did you talk about how much you appreciated him practicing (even though he hated it), or focus on the better sounds coming out of the instrument?
Praising effort was an odd mental shift for me as a parent when I started trying to do it with my kids. I'd always assumed that they would have that mental bridge connecting practice to success, and understand I was proud of their preparation when I praised good results. When I started saying things like you do a lot of practicing and I'm proud to see that or you worked really hard on that homework packet, great job or you really listened well to your ballet teacher at class today — with little or no judgment of the quality of their performance/grades/etc. — there was a subtle but noticeable shift. In their case they naturally have trouble focusing, and so supporting their struggle with that was a bigger boost than I'd ever accomplished by only talking about results. "I'm not good at anything!" still gets wailed occasionally when they're really frustrated, but it's much less frequent.
Meanwhile, look into activities that he's either naturally good at in some fashion or is intensely interested in. Try to keep it low-pressure (a lot of coaches/teachers also praise results instead of effort, not necessarily useful!), and let him take the lead to find a skill that you can encourage.