The Basic Structure
SUMIFS starts with the range to be summed, followed by criteria_range/criteria pairs. The order is the opposite of SUMIF, which explains most #VALUE! errors encountered when switching between the two.
Filtering by Date Range
For a rolling month, compare the date column to two boundaries: ">="&DATE(YEAR(TODAY()),MONTH(TODAY()),1) followed by "<"&DATE(YEAR(TODAY()),MONTH(TODAY())+1,1). Calculated boundaries avoid the need to touch the formula every month.
Absolute References
Lock your ranges with $ symbols ($B$2:$B$5000) before dragging the formula into a manual summary table. Without this, the range slides down row by row, and the totals at the bottom of the table become incorrect.
When to Move to Pivot Tables
Beyond three criteria and a few thousand rows, a Pivot Table or Power Query will be faster to recalculate and easier to maintain than a column full of SUMIFS.