ておく
te-oku
Not doing it now — parking it for later
The picture You do a thing now and set it down in place for later. Time gets pushed one step ahead of you. てある looks at a place already made ready; ておく is the hand making it ready.
Where the picture shows up in ておく
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read it in advance
会議の前に資料を読んでおきます。
kaigi no mae ni shiryō o yonde okimasu
I'll read the documents before the meeting.
Before the meeting starts, you set the papers you have already read and marked up on the desk.
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get it ready beforehand
ビールを冷やしておいて。
bīru o hiyashite oite
Put the beer in to chill, would you.
Hours before the guests come, you push the beer to the back of the fridge.
In speech ~ておく shrinks to ~とく: 冷やしといて.
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leave it as it is
窓は開けておいてください。
mado wa akete oite kudasai
Please leave the window open.
You stop your hand halfway to closing the window, leave the latch where it is, and step back.
Both 'do it in advance' and 'leave it that way' are ておく. Often it just means: don't touch it.
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say it in advance
部長に言っておきました。
buchō ni itte okimashita
I've already mentioned it to the manager.
Before the meeting-room door opens, you stop by the manager's desk, say your one line, and leave.
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write it down so it keeps
電話番号を控えておきました。
denwa bangō o hikaete okimashita
I noted the phone number down.
Before the call drops, you copy the number into your notebook and slip it into your pocket.
All of it in one picture
ておく is using your hands now to leave something in place for the you of later. Read the papers ahead and the meeting is light; put the beer in early and it is cold when guests arrive; leave the latch open and the air is still moving when you come back. Tell the manager first and nobody is surprised afterwards; write the number down and it survives the call ending. Whatever ておく attaches to, the action is not really pointed at now — it is set facing later.