Four pictures cover the whole rule set. Nothing else is hidden.
The numbers count runs of filled squares
Each number beside a row, or above a column, is the length of one unbroken run of filled squares. The numbers are in the order the runs appear, left to right or top to bottom.
Between two runs there is always at least one empty square. That is what keeps 2 2 from being the same as 4.
Crossing off is half the work
A square you have ruled out is worth as much as one you have filled — it narrows what is left. Mark those with a cross so you do not work them out twice.
Crosses are your own notes. They are never checked, and a finished picture is judged only on the filled squares.
A line is finished when its runs match its clue
Once a line holds exactly the runs its clue asks for, every remaining square in that line is empty. That is usually where the next move comes from.
Turn on the setting to fade finished clues and you can see at a glance which lines still have something left in them.
What you end up with is a picture
Every puzzle here is checked before it is published: a solver walks it using only single-line reasoning, and the puzzle is only kept if that finishes the whole grid. So there is never a point where the sensible move is to guess and see.
Because it finishes that way, the answer is also the only one possible.