I'm not sure where you get stuck with the help file. But I'll try to describe it in detail (I hope that I don't forget any step), maybe it helps. I remember that I also had some difficulties to understand how variables worked when I was new to AM. But this is only a short phase of confusion
For the case of a key there are even 2 possibilities. Either the player has to drag the key from the inventory onto the door (Instruction A), or the player clicks the door and can only get access to the next room, if he/she has the key in the inventory list (Instruction B).
A) Instruction for the case that the player has to drag the key onto the door to open it:
1. Create a bigger hotspot on door knob:
Make a hotspot around the door knob.
If you wish, you can also go to "audio" tab of the hotspot properties and add a sound of door rattling.
Or you can go to the "action" tab of the hotspot properties and check "display a text message" and add e.g. "The door is locked."
2. Pick up key:
This is what you already managed to do.
3. Let player use the key on the door:
Doubleclick the screen where the door is. Click on "Manage inventory items" (next to the key symbol). The Inventory Item List will pop up. Drag the key with your mouse onto the hotspot on the door knob. The hotspot properties pop up.
Go to the General tab and check "Go to another frame" and choose the frame with the open door, or the frame with the next room respectively. If you want the player to prevent to use the key again, go to the Action tab and check "Remove the dragged item from the inventory".
B) General instruction for all kinds of objects:
1. Create a hotspot for the case the key is not yet in the inventory:
Make a hotspot around the door knob. Rightclick on this hotspot to get access to the hotspot properties.
Go to "Variables". Check in the bottom half "The hotspot (or picture) must be enabled (or visible) only if..."
And click on "add" at "the value of the following variables is 0". Then select "new integer variable", type in the name of the variable (e.g. key) and click ok.
If you wish, you can also go to "audio" tab of the hotspot properties and add a sound of door rattling.
Or you can go to the "action" tab of the hotspot properties and check "display a text message" and add e.g. "The door is locked."
2. Create a hotspot for the case the key is already in the inventory:
Make a hotspot around the door knob on top of the other one. Rightclick on this hotspot to get access to the hotspot properties.
Go to "Variables". Check in the bottom half "The hotspot (or picture) must be enabled (or visible) only if...
And click on "add" at "the value of the following variables is 1". Select the variable (in this case "key") and click ok.
Then go to the General tab and select "Go to another frame" and choose the next frame (e.g. frame with open door or the next room).
3. Change variable to value 1 when object is picked up:
Now you must look into the hotspot properties of the key. You probably have already set it in the "item" tab to "When the hotspot is clicked, add an item to the inventory". And you probably chose the key.
Now go here also to the "Variables" and check the upper part "Change the value of one or more variables....". Then click on "add" at the "variables the value of which must become 1". Select your variable that you created (in this case "key") and check okay.
To prevent the player of picking up the key again, check in the Action tab "Hide and disable this hotspot" at the top.
If you still need help, I can make a small demo for door and key and upload it here, so that you can see the hotspot properties. Post if you need more help and tell me which case you need (drag the key or just click on the door).