Using both marks and registers in a single command means you mustn't mix up your ' and '' characters: the former is for marks and the latter for registers. So, ''ay'b means ``Yank from the cursor's position to mark `b', and store it in register `a.' ''
Finally, you can place the contents of any register with the put command (p). For example, ''hp will put the contents of register `h' under the cursor, beginning on a new line (a capital P will place it on a new line above the cursor).