As Orly said - if you clicked the helm, you have it, no matter how fast you clicked. It's in your equipment tab.
If you don't equip the helm, the game will give you the following hints, over the course of a minute:
When you pick up something, your character puts it in its bag. You can check it by clicking on "Items" (bottom left), or by pressing your 'I' key."
Your bag has three groups: Usable items (apple), equipment (shield) and everything else. Try finding the mining helm you just picked up.
Double-click the items in your bag to use or equip them. Christina will wait for you to put on your mining helm, so no worries.
and finally:
Press 'I' or click on 'Items' on the bottom left to open your bag. In there, find your mining helm by clicking on the 'Equip' icon (the shield), and then double-click it. If you have troubles, type:
/help equip
Try following these. ;P
Typing "/help equip" in particular will show you exactly where to click.
