can i help?

"Can I help you?" said Jane.

Though Jane herself had no inkling of it, those words were the keynote of her character. Any one else would probably have said, "What is the matter?" But Jane always wanted to help; and, though she was too young to realize it, the tragedy of her little existence was that nobody ever wanted her help... not even Mother, who had everything a heart could wish.

L. M. Montgomery

Jane of Lantern Hill - chapter 3

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i think when someone offers to help you - truly WANTS to help you - you should accept. even if you are doing something that requires a set skill level. if it turns out that if you hand it over to someone else, it will create more work for you to fix it afterwards, don't give them THAT job. 
it's like with a child. they are so eager to be involved in the "grown-up" things that you do. if they offer to help with dinner, you obviously don't give them the ingredients and leave the kitchen. but they can help stir or set the table or ...whatever. to deny a child their desire to be of assistance... i believe this crushes something within them. it's rejection. and good luck getting them to do anything when they are a teenager and more capable. you've already trained that willingness out of them.

it's really the same thing with adults. if a friend sees you working hard on something or struggling through something and says 'if there is anything i can do to help'... let them. even if it's just the mundane side stuff. speaking from personal experience, this can solidify a relationship. it's saying 'yes, i accept your offer and value you enough to involve you in this thing that is important to me'.

on the flip side, if you ask someone to help you, you are doing both of you a disservice if you don't spell out exactly what you want from them. if you are vague or say 'do whatever you want', which is fine, don't later on change around what they are doing or tell them they are doing it wrong. if you want something specific, be specific. if you made the mistake of not being detailed enough in the beginning and the help you are receiving is no longer what you need, it's not that difficult to let the person know that their assistance is still valued but your needs have shifted. to ignore this can destroy a friendship. 

above all, be grateful. when someone helps you, they are sharing a part of themselves with you. recognize that. let them know you appreciate them. everyone wants that validation.