Answer:
This is actually quite tricky.
In the simplest form, they are most commonly used with verbs of motion. An example would be "Climbing down" or "Putting away". Usually, many of these would be able to connect with said verb (Climbing Up/Down/Off).
Granted, while some can be used after a verb with no problem, other combinations need further additions to the idea, otherwise they become ungrammatical.
For example:
While some may need additions (Usually by adding nouns after the preposition):
"I walked up" -Ungrammatical
"I walked up the staircase. -Grammatical
Others will do fine without any, as they express a complete idea:
"I cleaned up" -Grammatical
"I cleaned up the house" -Grammatical
There are even irregulars. These ones modify the meaning in slightly different ways.
"Cool off/down"
"warm up"
Then the weirder ones that may be rephrased and would still be grammatical such as:
"I ran up the stairs"
"I ran the stairs up"
You may even want to play with prepositions vs. phrasal verbs such as:
"He ran up a hill" (<em>u</em><em>p</em> is a preposition)
"He ran up a big bill" (<em>r</em><em>a</em><em>n</em><em> </em><em>u</em><em>p</em> is a phrasal verb)
Granted, while these may not have been possible before, the rule of language is that its interpretation is based on what the vast majority view it as.
While there are some rules you might be able to follow, some of it just depends on semantics.
