The first thing to remember is that they are no different from electrical mowers with regards to their need for cleaning after each use. Leaving damp or dry grass on the blades will speed up the degrading process and increase the risk of rust. Wiping the mower with a damp cloth is the best method to remove all grass and mud. Don't use anything sharp or metallic, it will scratch the blades which will cause them to become blunt quicker.
It is worthwhile to take the time to clean the whole machine as well. Even though it is only the blades which do the cutting work, rust can spread throughout the machine's metal. Even if you think a little dirt on the handle or on the side may be harmless, if left neglected it will spread to the more important parts of the hand lawn mowers such as the blade. This is one way that it differs from an electrical mower which has plastic parts in between the metal of the blade and other parts.
Once the mower is completely wiped, use a cloth to dry it. This step can be skipped if the weather is hot enough, because it will then dry in a few minutes. However, if you're unsure, it is always best to dry it manually. The longer the time the metal is left damp, the greater its risk of experiencing long-term damage. Once you've taken the time to get the mower clean, make sure it is stored in a cool, dry place and is well covered by a plastic sheet. This will prevent it from getting damp again.