You need to collect three machine parts.
First, head to the right, down, left and down, and continue right to the stairs. Jump up, and proceed right until you see three spring boards. Jump up.
Head left to collect the first machine part; you will need to duck to avoid being killed by the crushers. Continue left past the crushers until you see two wingnuts spinning up and down. Get past then and collect the second machine part.
Return to the springboards and continue right. Climb up, and look for the third part to the left. Now, drop down the right side.
Your path left is blocked by a spinning ufo, which is the only enemy that kills instantly on touch. Put the three machine parts in the machine, and the spinning ufo will be pulled down. Jump over, and continue left and drop down.
Head left to get the door key, then head all the way right to open the door.