You would do binary long division. You need to use unsigned numbers since you can't 2's complement an arbitrarily large number... just follow the usual rules for negatives (i.e. -/- = +, +/+ = +, -/+ = -, +/- = -) once you do the unsigned version.

Wikipedia:

The following algorithm, the binary version of the famous long division, will divide N by D, placing the quotient in Q and the remainder in R. All values are treated as unsigned integers.[citation needed]]]

if D == 0 then throw DivisionByZeroException end
Q := 0                 initialize quotient and remainder to zero
R := 0                     
for i = n-1...0 do     where n is number of bits
  R := R << 1          left-shift R by 1 bit    
  R(0) := N(i)         set the least-significant bit of R equal to bit i of the numerator
  if R >= D then
    R = R - D               
    Q(i) := 1
  end
end  

You can do binary long multiplication for multiplying as well... although there are better algorithms for very large numbers of bits.