Assuming A is Date, B is amount and C is YTD and Row 1 is headers:
In C2 put =B2 - gives you the total of the first amount
In C3 put =B3+C2 - gives you the previous YTD plus the current amount - and drag (or copy) down as far as you need
Edit
I assume you are not asking how to copy/paste; to drag the selected cell hover your mouse over the little black square at the lower right of the cell until the pointer changes to a cross, then drag down as far as you need; references in the dragged cells will remain relative.

If you double click on the drag handle, it will fill down to the end of non-empty adjacent cells.
The image shows OpenOffice, but LO behaves the same.
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