Most of the time "into" is what you want, which is why the two-word version looks like a typo when it is actually correct. "In to" arises when "in" belongs to the verb before it and "to" belongs to whatever follows — they are neighbours, not a unit. The classic example, "turned himself in to the police," means something quite different from "turned himself into the police."
A single preposition expressing movement toward the inside of something, or transformation.
Two separate words. "In" completes the verb; "to" belongs to what comes next — often an infinitive.
Into is a single preposition showing movement inside something, or a change from one thing into another: she walked into the room, the caterpillar turned into a butterfly. In to is two separate words that just happen to sit next to each other: in belongs to the verb, and to starts what comes next.
That happens most often in two patterns. The first is a phrasal verb followed by to: hand in to the teacher, give in to pressure, turn himself in to the police. The second is in followed by an infinitive: he came in to talk, she stopped in to say hello, where "to" means "in order to".
A quick check: if you can add "in order" before "to", write two words. "He came in (in order) to talk" works, so it is in to.
He came into talk about the schedule.
✓He came in to talk about the schedule.
This means he came in, in order to talk, so two words.
She walked in to the conference room.
✓She walked into the conference room.
This is movement inside a place: into.
The suspect turned himself into the police.
✓The suspect turned himself in to the police.
He turned himself in (surrendered) to the police. "Into" would mean he became the police.
Quick way to remember
Check whether "in" belongs to the verb. If the verb is "log in," "give in," "turn in" or "come in," then "in" is part of the verb and "to" is separate. If the sentence is about going inside something or becoming something, use "into."
Is it "log in to" or "log into"?
Both are widely used. Many style guides prefer "log in to your account", because "log in" is the verb and "to your account" is where. "Log into" is common and increasingly accepted.
What about onto and on to?
The same logic applies. Onto means movement to a position on something (the cat jumped onto the table). On to is on as part of a verb plus to (let's move on to the next item).