Overlap is the first technique to use in almost every ursograma: push the groups to the left, then to the right, and compare. The cells that the same group fills in both positions are definitely filled, whatever the solution.
In How to play you saw it with a single number. Here is the full technique: with several numbers, with what is already decided on the line, and in colour.
Start with a single number on a line that is still empty. Count the cells left over after placing the group: that is the slack. From the group pushed left to the group pushed right, it moves by exactly the slack. The first cells of the left position, as many as the slack, are left behind; the rest are filled in both positions. You can fill those straight away: they are the length of the group minus the slack.
6 | ·········· (the line)
6 | 111111···· (pushed left)
6 | ····111111 (pushed right)
6 | ····■■···· (certain so far; · undecided)
In the end, the 6 is still a 6: the line will have six consecutive filled cells. What you don't know yet is where. For now, only these two are certain, whatever the position of the group; the other four stay undecided until the columns crossing the line give you more information.
When the number is no more than half the line, the slack is enough to separate the two positions completely, and there is nothing you can fill yet. A 5 in ten cells doesn't let you fill any; a 6 lets you fill two.
With several numbers you do the same, but you push the whole line: each group as far left as possible, with one empty cell between groups; then the same on the right. The slack is what is left of the empty line after adding up the numbers and the required gaps between them, and it is how far each group moves from one position to the other. From each group you can fill its length minus the slack straight away: the last cells of its left position.
4 2 3 | ············ (the line)
4 2 3 | 1111·22·333· (pushed left)
4 2 3 | ·1111·22·333 (pushed right)
4 2 3 | ·■■■··■··■■· (certain so far; · undecided)
Working out the slack is the sum you do in your head when you look at an empty line: add up the numbers, add one for each gap between them, and subtract the result from the length of the row (or the height of the column). Every group bigger than the slack lets you fill something straight away. When the line already has Xs or filled cells, the sum no longer works: you push the groups as shown further down.
A cell filled in both positions only counts if it is filled by the same group. If on the left it is the second group passing through and on the right it is the first, the coincidence proves nothing: there are solutions where the cell stays empty.
3 1 | ······· (the line)
3 1 | 111·2·· (pushed left)
3 1 | ··111·2 (pushed right)
3 1 | ··■···· (certain so far; · undecided)
Pushing a group means placing it as far left (or right) as it can go. An X in the way pushes it further along; a cell already filled holds it in place, because some group has to cover it. The two positions get closer, and the overlap gives you more. A filled cell next to the edge is the strongest case: see From the edges.
4 | ··×······· (the line)
4 | ··×1111··· (pushed left)
4 | ··×···1111 (pushed right)
4 | ×××···■··· (certain so far; · undecided)
3 | ··■······· (the line)
3 | 111······· (pushed left)
3 | ··111····· (pushed right)
3 | ··■··××××× (certain so far; · undecided)
This second case is the other side of the technique: besides the cells the same group fills in both positions, the cells that no group reaches in either position stay empty.
In colour, two groups of different colours can sit side by side, with no gap between them. When you push the line, you only leave a gap between groups of the same colour, so the slack can be bigger than the same numbers would give in black and white.
3 2 | ······ → ■■■×■■
3 2 | ······ → ·■■·■·
That is how an ursograma moves forward: overlap on a row fills a cell, that cell goes into the column that crosses it, and the column now has something to push.