Opening it is simple. Remove the grip, grasp the portion of the shifter that turns to shift, and rotate it back like you are shifting, while pulling it towards the center of the bar.
Putting it back together is not simple, and will likely not happen without assistance. Ask your LBS to show you the procedure if you want to learn.
If not, ask them to fix it. It will like require replacing the pawl spring (snoopy spring) inside it, which creates the click, and holds the shifter to a particular gear. It may require replacing the shifter body, depending on what is broken inside.
- Shimano Installation guide
- Shimano tech docs for RevoShift 3 speed
- Other styles of RevoShift Tech Docs
The third link takes you to a tech doc page. It's java, so I can't link to the search directly. Type RevoShift in the search box.