Trim the stems. Asparagus has a natural "breaking point" at the woody part of the stem. Trim the ends by breaking the asparagus with your hands at this breaking point, or trim off the white ends of the asparagus with a knife. Discard the ends.
Place the trimmed asparagus stalks in a glass jar, in an upright position.
Fill the jar with about 1 inch of cold water, just enough for the bottom of the stalks to rest in the water.
Place the asparagus in the fridge. Storing the asparagus in the right place in the fridge is essential. Avoid placing the asparagus near the ice maker (if that's inside your fridge) or the back, as these are the coldest spots and will cause the asparagus to freeze.
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Notes
There's no need to wash asparagus before storing. Before use, rinse the asparagus under cold water to remove any dirt or debris.