I was not aware Amazon will even wrap gifts for you - how much does it cost to do that?  I too hate wrapping and I'm not very good at it lol.
		
		
	 
First, click on your Amazon cart icon in the top right corner.  Under the Subtotal in the top right corner, check the box "This is a gift order" and then click the yellow "Proceed to checkout" button.  This will hide the prices on the delivery receipt.
Second, under each item, there is a little tiny gift box icon that says "Add a gift receipt".  Click on that button & a "Choose gift options" box will appear.  This is where you can write a note for each item (ex. "From purbeast0 to my favorite nephew").
Third, in that same popup, check the box "Gift Bag/Box".  Prices vary based on the size of the gift (I think some stuff can't be wrapped, like if it's particular huge or heavy), but the small stuff is usually like $3.50 per wrap (or bag) & goes up from there.  I sent some R/C monster trucks to my nephews & it was $4.50 to wrap each one, and those were like 18" boxes.  So about the cost of one nice roll of wrapping paper per item...not cheap, but otherwise I would have had to have them shipped to me, wrap them, then re-ship them to them on the other side of the country, or just ship them directly in the box, which would have been kinda lame for little kids haha.  Never thought I'd be paying for convenience, but here I am 
 
The funny thing is I've started to do it in other aspects of my life too.  I've got a ton of family in town & I ended up hiding all of the plates & cups & stuff and just using disposable paper & plastic everything...throw it all away afterwards (hey, we have a good recycling program here! haha) & have had zero dishes to do lol.