a 10 or 11 yr. old should concentrate more on growing up and having fun than looking for a job. when that time comes for real, you will know enough to have some idea what truly interests you. if you just have to have a job, do something you think you will enjoy learning.
A paper route. I had one at about that age. It's decent pocket money and it teaches responsibility. You can't just go run off to your friends house to hang out when everyone's counting on you for their paper.
Depends what kind of job you mean. You're not actually allowed to get a proper job until you are 14, or 12 if it is with a family business. You should talk to your parents about pocket money (they always have stuff to do) if you don't already get it, or ask around your neighbourhood (only if you know people of course!) for jobs as well. Mowing the lawn and stuff should work if you're really desperate.
I don't really know of any "real" jobs for a ten or eleven year old. To be honest, there really isn't any job for a kid to have. But you could do chores and ask your parents to pay you! That's what I always do, and I make good money!