In normal way,You must construct a truth table,An 4*4 bit multiplier need eight-bit outputs,Construct equations for each out bit,Simplify the equations.Then you can build the circuit only with logic gates.
There is an easy way to build the circuit,An 4*4 bit multiplier has two four-bit inputs and eight-bit outputs,You can use a 256*8 bit ROM to do this,high four-bit of address and low four-bit address are inputs,DATA of the ROM is outputs of the multiplier.