Start with a normal with the same mean and variance, perform an appropriate test to see if the fit is adequate, if it is stop you have you distribution. If it is not adequate look at the data, is there something about it that you recognise, is it multi-modal, is it heavy tailed, skewed, ..

If nothing suggests itself from an examination of the data or for theoretical reasons consider Kernel Density Estimation (Google for it if you need more information).

CB