The plastic rim protection is flexible. It has to be forced by some bending it up pressing one corner on the rim and it will be possible to press on completely.
Important as Frank wrote, good irons with no burrs. Make sure to not bend with the iron in wrong angle, it has to be flat against rim.
Use good iron too. I have a curved model that work fine.
I have also used a pieces of 1/2 oil hose as rim protection, seen on one photo.
When tire is on half ways, tube is going in. Make sure to fill tube with a little air so its not really flat. Its way too easy to pinch it and you have to invest in new tube. Have a soft curved wood stick to puch away the tube where you set the iron before you start to wrap it on the rim.
Use good rim lubricant. I have used soft soap for floor cleaning until this year when I started to do it by myself with real tire lube.
Another thing is how the tube valve nuts has to be. I started a thread about it yesterday.
http://forums.sohc4.net/index.php/topic,171478.0.html