Be gentle and go slowly, but don't be afraid. You can do it. If you don't have a spudger (basically just a very thin plastic or metal object to pry with - I like one called an iSesamo) any similar object will do. Someone suggested a very thin flathead screwdriver. Someone else used a guitar pick. A thin knife blade is good too - but be careful not to cut yourself.
The trick is to put it into the slot apply gentle pressure pushing inward and twist - one part pushing up against one half of the shell and another part pushing down against the other half. Don't be discouraged if this doesn't do anything. Move the blade an inch or so along the slot and keep trying. Keep doing this all the way around. This remote has several spots along the inside of the slot where tabs fit into small slots that will give way and open once you hit the right spot. Once you've got it a little bit open in one place, you've got it. Keep doing the same and you can't miss.
After you have opened it up, done your repair job and snapped it shut, you may find little nicks in the plastic. This is only cosmetic, but you can often make these nicks go away by scraping at them with a thumbnail or butterknife.
Go for it and good luck!
