I don't understand convolution, and I would love to see some worked examples
First off, visualizing how these this function works graphically can be a big help. The first function is 'slid' past the second function, the area of the two defines the height of the third function


Source Wikipedia: https://upload.wikimedia.org/wikipedia/commons/9/97/Convolution_Animation_%28Boxcar%29.gif

Hint:
Sometimes its best to draw the functions, a dirac delta function times a dirac delta function is dirac delta function (and dirac delta functions simply copy whatever function they are convoluted with)