Three of the most useful heuristic rules I've learnt:
(1) When trying to define a morphism that has to make a diagram commutative, first forget about signs: in the end, they will agree.
(2) If you want to prove something using induction, first check if it works (besides for n=1) for n=2.
(3) Trying to define a morphism that has to fulfil some universal property? -The first one (diferent from zero or constant) that you can imagine / find is probably: (a) the only non trivial one that exists, (b) that miraculously fulfils also your requirements.