Step 1 of 5
Join the neighbors
A cell with only two ways out has no choices left: it joins both.
The rule of thumb: Every cell links to two neighbors along the path; when a cell has only two it can still reach, join both.
Stop thinking about the route and think about links. The path passes through every cell, so each cell is joined to exactly two side-by-side neighbors: the one it came from and the one it goes to. Only dot 1 and the last dot have a single link.
So count the exits. A cell that needs two links and has exactly two neighbors it can still reach has to use both, even before you know which way the path travels through it. Dot 1 works the same way with one link: if only one neighbor is left open, that is its way out. Draw those links in your head and short stretches of the path appear for free.
The links you find also take away options from the cells beside them, so the next one is often easier. These practice boards are picked so that you cannot finish them without chasing exits this way.
Where to look: Cells squeezed against the edge, against a dot you have already used up, or against a link you know about. Count the open neighbors: two for a middle cell, one for dot 1.
Worked example
A real position from a board that needs Join the neighbors. Purple ring: what the reasoning rests on. Grey line: links already known. Dashed: the edges in question. Green line: a link it proves. Red cross: an edge it rules out.
That is the exit-counting habit. Next: what a cell does once it has all its links. Step 2: No branches, no traps →