Which is correct: "Set up something" or "Set something up" or "Setup something"?

As a programmer, I often have to use this expression:

Set the application up.

or something like that. But I'm not sure what the correct grammar is, and what this grammatical area is called in English.

Both "set up something" and "set something up" are perfectly correct English, as "set up" is a phrasal verb. As kajaco mentions, "setup something" is just a spelling error (although it is fairly common).

Of the two correct phrases, I don't think one is inherently more clear than the other, if the something part is short enough. But, it is important not to let the two words separate too far. That is, when the something part gets longer, it becomes increasingly worse to separate "set" and "up".

For example, these sound good, because "all of your accounts" is short enough:

• I will set all of your accounts up. / I will set up all of your accounts.

But the following only really works if you don't separate the phrasal verb components:

• ?I will set a table of all the people who haven't logged in since May up. (sounds awkward)

• I will set up a table of all the people who haven't logged in since May.

If you are a non-native speaker, you might ask, "what is the line between too long and not too long?" Well, there is no clear line that can be given as a rule. But I would say that if the something part is more than 5 words, you might want to play it safe and keep "set" and "up" together.

"Setup" is noun, not a verb, so you wouldn't "Setup something".

"Set up something" keeps the two parts of the expression (set and up) together, so that seems clearest.

Other wording might work better: Install or initialize.

Somebody did a pretty extensive analysis of this at "Setup" Is Not a Verb. You can probably guess from the title what the conclusion was!