First open then bracelet at the buckle, so you get easier access to the case back. Just push the springbar in with a springbar tool or a similar object. I used a sewing pin this time, as I don't had a spring bar tool with me.
Now you can start unscrewing the 6 small screws on the side of the bezel. Carefully store these tiny screws somewhere safe. I always use the lid of my screwdriver box. There will be more screws, so remember what comes from where.
For removing a dead battery, it does not really matter how you do it. I usually use my metal tweezer, but, of course, for installing a new battery, you use a plastic tweezer. If possible even take it out of the package with your tweezer. When you push down the lock, it will lock automatically. Most of the time you even hear a click when the lock is back in place.
If needed, re-grease the gasket with a silicon based grease. Just a little bit, to keep the rubber in shape and to help the watch stay water resist.