MacBook Unibody Model A1278 LCD Panel
Removing the glass front was difficult at first. I used a cheap suction cup (not from ifixit) but the glass didn't come off at all. At some point the suction cup broke, the rubber just came off. So I used a hair dryer and a credit card to get into the lower right corner. I started by placing the credit card in the small opening between the edge of the glass and the rubber lip (at right angle). Then I carefully and patiently dug into the corner, and as soon I was in I could carefully detach the glass from its adhesive (frequently using the hairdryer). Maybe I was just lucky, but for me this worked fine.
The rest was pretty easy (except reconnecting the LVDS which was a pain at first; see my other comment). I used permanent double sided tape to put the glass back on, which seems to work just fine.
There are other guides for replacing the LCD on the 13" Macbook unibody without removing the whole display assembly. I tried this and had some problems when it came to reconnecting the new LCD to the LVDS. The main problem with this is that the LVDS connector cable is very short and therefore there is not a lot of room for plugging it into the LCD. After a while I decided to follow the ifixit guide and remove the display assembly. This made things very easy since I could push the LVDS cable back a little which gave me enough room for reconnecting the LVDS easily.