The most important tip is that you solve the puzzle by starting in multiple places at the same time.
First search for the hexagons with only 2 free entrances. You can already draw a piece of the route in those hexagons. And sometimes the pieces of the route are already connected to each other.
See example 1.
The next step is to connect the route pieces together. Here you must keep in mind that no 'loose' ends can arise. In example 2 you see faulty connections, creating 'loose' ends that can no longer be connected to anything else.
Also note that you do not suddenly have 2 routes at the end.
And when you have connected all the pieces together, one route remains. See example 3.
Start with the easy puzzles with one 'hedge star' to get familiar with the puzzle. With the difficult puzzles you sometimes have to come to a solution through logical reasoning.
Some puzzlers draw the route intuitively, but there is a risk that things will turn out wrong. Making the puzzle with a pencil and an eraser is handy in that case.
Have fun puzzling!