Most important is the correct timing: The 3 days leading up to new moon between autumn equinox and winter solstice i.e. New moon happens at the same moment across the whole planet, however we would strongly advise that one stops cutting at least 10 to 15 minutes prior to the proscribed new moon time just to be safe.
We normally publish the accurate time of felling on our website.

Cut so as to fell the tree/pole down slope so that the cut stem of the tree is at a higher point than the end. This helps with the drawing of the sap to the extremities of the tree for faster and even curing of the timber.

Once felled, it is best to leave all the bark and as many branches as practically possible on the tree. For large timbers we recommend leaving the felled trees (typically in the forest) for 3 months with all branches and bark still intact. This is to ensure the timber cures properly, which will leave the timber practically free of splitting and warping. It will also be much lighter so will be much easier to extract from the forest, with less fuel used in transport.
In leaving as many of the branches on as possible, it is particularly important to leave the top of the tree intact when felling, as the branches and top, help to pull the sap (which may still contain minute traces of starch, which is the food insects and fungus are after) out to its extremities. This also helps the timber cure more efficiently and evenly, making for a more stable timber. Note that this only works when the timber is cut at the right times of the year, as otherwise insects will attack the timber.

Remember regular foresters are used to cutting trees up into logs with all their limbs dismembered….they often cut all the side branches off before felling the trees so you need to get them to trim as little as possible and then they also cut off the crown when it is felled ….so you have look out for that and explain carefully how you want it done so as to get the guys to age the trees with their branches.