I'll review, then give a few more examples, from Stargate SG-1, looking at the question from a slightly different angle.
The easiest phrases to distinguish, as skroberts demonstrated, are the infinitive verbs.
Daniel's office door was open, so Jack wandered in to cause trouble and be generally bothersome.The infinitive verb is to cause, and there's no such thing as into cause, so using in to is easily decided.
skroberts also covered prepositional phrases involving to.
Ferreti tuned in to what Sam was saying just in time to avoid the trap.The prepositional phrase to what Sam was saying serves a separate function than the in, and should be separate.
Another way to look at this sentence is to back your focus up a bit: tune in is a common verbal phrase. When there are common verbal phrases like turn in, invite in, give in, or step in, the in remains separate from the to. The tricky part is, some of these verbs can also be used with into, when your meaning is different.
The preposition into generally indicates movement towards the inside, or a transformation. If your meaning is not one of these definitions, you usually want the separate to. Let's practice with a few:
Walter waved the memo in his hand. "Let me just take this in to General Hammond, and then I'll be right with you."In the first example, Walter is taking the memo to General Hammond, and the construction shows that he's outside of where Hammond is and going in. But he's not in any way going inside General Hammond himself. In the second example, he's going inside General Hammond's office to leave the memo there.
Walter waved the memo in his hand. "Let me just take this into General Hammond's office, and then I'll be right with you."
Vala timed Daniel's walk down her corridor just right to invite him in to dinner.In the first case, Vala is literally inviting Daniel to enter her room; she's not expecting him to get inside the food! In the second case, Vala is moving from being an outsider with SG-1 to being an insider.
Vala was touched that SG-1 invited her into their group.
"Turn" is a verb commonly used with both in to and into, but the usage can easily distinguished by meaning.
Jack tells SG-9, "Turn your weapons in to the armory before your debriefing."In the first example, turn in is a phrase meaning to give or return something to someone or somewhere. In the second example, turn into is a phrase meaning that something will be transformed into something else.
Jack tells SG-9, "I wouldn't wave your P-90s around. The Nox might turn your weapons into flowers."
I hope this and skroberts' original post give you what you need to decide when to use in to versus into.