When hangul is handwritten rather flowery it is referred to as 흘림체 or "cursive". Here is an example of a mild 흘림체 vs it's typewritten counterpart:
In paraphrase of this article note the following when it comes to handwritten hangul.
Strokes are more important than shape
To read handwritten Korean, one must see the pen/brush strokes, not the final shape. There are always stray markings when handwriting, but they are artifacts of following a very consistent, intentional pattern of writing the shapes.
In the end, rather than focusing on perfect circles or straight lines ...right angles...look only for how the [pen, pencil, or] brush traveled across the page
You can easily master the order to each symbol as writing always starts in an upper corner and progresses to lower, opposite corner (when working with brush and ink, one would not want their hand/arm in the ink, so the direction is logical).
Violating the order of strokes makes writing illegible.
Here is a diagram showing the stroke order. Use it to try to decode some handwritten Korean.
For more stroke guidance, try this site which will demonstrate each character's order of strokes.
To answer your question, using this proper, standard way to hand write characters is paramount.