First, find a good axe that fits your body, and has a suitable, properly sharpened head for the task. The head weight, balance, haft length and shape all affect 'fit'. Lacking someone to help who knows axes, try various axes in your hands to see which feels best to you as you slowly and smoothly make short swings at imaginary targets. One bit of good news is that the better makers have evolved their axes over many years and by following the manufacturer's suggestions, you won't go too far wrong (don't buy a three and a half pound felling axe for day hikes).

For heavy cutting, like felling or splitting, start with one hand near the 'fawn-foot' at the bottom of the haft and the other a comfortable distance toward the head. Swing smoothly toward the target while sliding the upper hand toward the stationary hand (at the bottom). After a few strokes, you will start to develop a smooth, accurate stroke. Don't try to force things - let the axe do the work.

Lighter cutting, like most limbing and small splitting, can be done with one hand, obviously employing a smaller, lighter axe. Lots of practice, again concentrating on letting the axe do the work, will pay off in saved energy and fast, efficient cutting.

For some work, you might use two hands on an axe primarily meant for one handed use. An example of this would be felling a small tree with a medium camp axe. The converse is sometimes the case, such as light limbing with a Hudson's Bay pattern axe, like the 'Scandinavian Large Forest Axe' by Gransfors-Bruks.

The U.S. Forest Service has videos and manuals that cover axe work in much greater detail and from a much broader knowledge base than I possess. Hope this helps...