Assuming the column with the counting integers is in column A...
each cell in column A is in a row. the rows are numbered 1 thru n where "n" is the current size of the table.
If the first row is a header row for titles and identifying the information in a column then you will start entering in row 2.
A2=row()-1
this is shorthand for .... select cell A2, then type (or copy and paste from here) the formula:
=row()-1
select cell A2, copy
select cell A2 thru the end of the column, paste
Another way is to enter the counting numbers starting in cell A2 like this:
1
2
3
now select cells A2 thru A4
now hover the cursor over the bottom edge of the selection in the middle. a yellow dot should appear. Grab the yellow dot (click and hold), then drag down to fill as needed. This technique works for numbers, dates, week days, month names, durations, etc. My preference is that the first method I presented is better.