There are two ways to do this. One of them is much harder to get wrong, and it is not the one most people reach for first.
This is the method everyone knows. Divide the shape into rectangles, measure each, multiply each out, add the results.
For a straightforward L-shape it works well. Draw a line across the inside corner to split the L into two rectangles, measure both, add. Two rectangles, four measurements, one addition.
Where it gets fragile is anything more complex than an L. Once you are dealing with four or five rectangles, the failure is not the arithmetic, it is the bookkeeping. You measure a section, get distracted, and either measure it twice or not at all. The number you end up with looks entirely plausible and there is nothing in it that flags the mistake.
This is the one worth knowing. Instead of building the shape up from pieces, measure the full rectangle the room would be if the missing corner were filled in, then measure the missing piece and subtract it.
For an L-shaped room: measure the overall length and overall width as though the room were a complete rectangle, multiply for the bounding box area, then measure the two sides of the cut-out corner, multiply, and subtract.
It is more robust for two reasons. There are fewer numbers to keep track of, and the sanity check is built in. The subtracted piece must be smaller than the bounding box and the result must look plausible against the space you are standing in. A bookkeeping error in method one produces a number that looks fine. The same error here usually produces something obviously wrong.
Bounding box and subtract for shapes with one or two missing corners, which covers most L-shaped rooms, chimney breasts and boxed-in pipework. Split into rectangles for shapes with pieces added on rather than removed, like a room with a bay or an alcove. Whichever you use, sketch it first.
Draw the room roughly on paper, not to scale, before taking a single reading. Then label each wall with a letter, and write each measurement onto the sketch as you take it.
This is the entire difference between a five minute job and a twenty minute one. The common failure with awkward rooms is standing there afterwards with seven numbers and no reliable memory of which wall each came from. A rough sketch with numbers written on it as you go is a record. Seven numbers in a phone note is a puzzle.
Mark the split lines on the sketch too, and shade the piece you are subtracting. When you come back to it, the method is visible rather than remembered.
Angled walls, curved bays and rooms that are subtly out of square need different handling, and it is worth being honest about which are practical.
A diagonal wall creates a triangle. Measure the two sides that meet at the right angle, multiply them, halve it. Add or subtract that triangle as appropriate. If there is no right angle to work with, measure all three sides and the area is still solvable, but at that point a floor plan app is faster than doing it by hand.
A bay window is usually a trapezoid, which is the average of the two parallel sides multiplied by the depth. Close enough for material ordering. Not close enough for a fitted seat.
A curve is not worth doing by hand. Approximate it with a rectangle that splits the difference, add a generous waste factor, and accept the approximation.
A room that is simply skewed, with no parallel walls anywhere, is the one to check with diagonals. If the two corner-to-corner readings differ by more than an inch or two, treat every area figure as an estimate and order accordingly.
Two checks, both quick.
First, measure the full bounding box even if you used the splitting method. Your total must come out smaller than the bounding box, and by roughly the amount of the missing corners. If it does not, something has been double counted.
Second, sanity check against a room you know. If you know your living room is 200 square feet, and this awkward room clearly feels smaller but your arithmetic says 260, the arithmetic is wrong.
On material ordering, remember that the waste factor for a room with multiple angles runs higher than for a simple rectangle, commonly around 15 percent against 5 to 10 for a plain room, precisely because there are more cuts and more offcuts that cannot be reused. That extra allowance covers a lot of measurement imprecision. The full room method is here, and the square footage basics are here.
If you would rather just be told what to buy, our best laser measures are on the front page.