The students' hands were tired from writing. Here we have more than one student whose hand was tired from writing. There is one important exception to this rule. This seems nutty, but is actually for a good reason. One important thing to note is that you never need an apostrophe to just make something plural.
Every sentence needs both a subject and a verb.
If your sentence is missing one of these, it is a fragment. The black cat with white paws on the windowsill. We still need a verb, so this sentence is a fragment. Goes on happily down the winding road. We still need a noun, so this is a sentence fragment.