Before you do anything else, check overhead for dead branches which may fall and injure you, and for things like hornets nests. Clear the area around the tree of any undergrowth or branches that could deflect your blows. If the tree has a particularly large spread of roots or boles around the base you may want to construct a platform so that you can reach a thinner part of the trunk and save time and effort. Obviously if you do this make sure the platform is stable and you have a clear route of escape (in case something goes wrong!).
Cut from both sides of the tree. First you chop a notch out at an angle of about 45 degrees and then another on the opposite side at a lower level, on the side which you want the tree to fall. Do not cut through more than half the tree before starting the other notch. You must work at a height that is comfortable for you. Try to cut downwards at 45 degrees (you may need a horizontal cut occasionally to clear debris etc.).
A steady rhythm of blows will cut much more efficiently than fewer big blows. If you put too much effort behind the axe your aim will suffer, you will tire and then every swing becomes more dangerous. Always let the weight of the axe do the work.
Alternating the angle of the stroke will prevent the axe from jamming. Too steep an angle will cause the axe to glance off, end-on will make the axe jam (or simply be inefficient). Try to aim for a 45 degree angle.