The conditions required to have an well-defined ordering are simply:
Antisymmetry: If a≤b & b≤a then a=b
Transitivity: If a≤b & b≤c then a≤c
Connexity: a≤b or b≤a
Of course, this doesn't guarantee it makes sense in context with all the other operations, as you it'd be well-defined to say 1≥2≥3≥4... If you're talking about a group, then an ordering requires additional conditions like: If a≤b, then a+x≤b+x for all x. Anyway, hopefully that makes more sense. For a taste of what a non-orderable set looks like then, one need only consider the complex numbers. They 'get bigger' in 2 dimension…