Question: Hiding PART of a layer in Photoshop CS6?

[Hot_Swap_Fries]

So I'm making an image for a friend and I need to add a mustache to someone, but their finger is in the way of their upper lip. How would I go about adding the mustache in the right spot, then running a tool or something over it to remove ONLY the parts that is being covered?
 

 

[Evolution.]

I would recommend using MS Paint 

[DrMacintosh]

I mean I am certified in Photoshop CC but I'm not entirely sure what you mean. 

[Hot_Swap_Fries]

This will look weird, but this is what I'm talking about. Say I want to move the sombrero behind her, but still keep the parts that are not covered by her visible, but the rest is hidden. How would I go about doing this?

[vanished]

a Layer mask most likely

Use your favourite area select tool to grab the white of the background and make a mask using the selection.  Then move that mask from the background layer to the hat layer, unlock it so you can move the hat without moving the mask, and put it in position.  Then you could adjust the mask with the brush to fill in the parts you do or don't want.

[Evolution.]

3 minutes ago, Hot_Swap_Fries said:

This will look weird, but this is what I'm talking about. Say I want to move the sombrero behind her, but still keep the parts that are not covered by her visible, but the rest is hidden. How would I go about doing this?

by dragging the sombrero out the way 

[LordLeewee]

in that pic youd move the sombrero, change the opacity so you can see the image behind it, use the lasso tool to cut out the bits of the sobmbrero you dont want and delet them

[Arika]

you have to erase/delete the parts of the image/layer you dont want.