This part can be tricky depending on your radio. This is how I took apart mine.
I first unscrewed the back.
After that the only thing holding in the board was the volume nob. If you're lucky the top of your knob will come off (no pun intended). If you look at my board you'll see the "buttons" on my radio are nothing more than some common momentary switches. I even have a little LED there as well. Bonus!
Now the volume nob on my radio would not come off, so I took a different approach. Using some tin snippers I cut apart the plastic case until everything was free. Then I used some little wire clippers and cut the remaining bits away from the knob area. You should wear eye protection during this part as plastic was flying everywhere.
You'll notice that I saved the "Battery Holder" area. Do this as you can. You can just buy a AAA holder for $1, but we're on the cheap here people!
In the end you should have, if nothing else, your radio's circuit board out, and if you're lucky you'll have a battery holder as well.