Think of the process as flipping one signal across the y-axis and then sliding it across the other signal, multiplying the aligned terms and summing the results at each step to find the values of the output sequence. Using a tabular method is easiest for convolution sums using short sequences.
Write the values of one sequence from left-to-right across the top of the table. Write the values of the other sequence from top-to-bottom along the left side of the table. Now, fill in the table with the product of the values at each row/column intersection. Starting at the top-left of the table, sum each diagonal (sum the products only, not the orignal sequence values at the top and left of the table) . These diagonal sums are the values of the output sequence.
I can post a picture/example when I'm at a PC if that will help.