I've seen lots of threads debating the merits of sending your HRM back to Polar for battery replacement, having a watchmaker do it or doing it yourself. Didn't come across any how-tos so I reckoned I'd post a quickie on this particular model.
First let me say that with an S150 you'd be a total sucker to have Polar do it for $40 or whatever. Super simple - the guy at the watch shop in the mall could do it in his sleep. You'd have to be pretty mechanically untalented to not be able to do it yourself.
You'll need a micro-screwdriver set (like they sell in the checkout line at Ace for fixing eye glasses, etc.) or some other very small phillips screwdriver. You'll also need a CR2032 watch battery. Radio Shack has them or easy to get online.
Lay the unit face down on something soft so you don't scratch it. Take the four screws in the corners on the back out. I recommend doing this progressively (do each one half way, then go around doing a few turns on each). There are a couple of springs in there that are held down by the back - see picture. In mine they seemed to be captured but I could see them popping out if you weren't careful. Once you have the screws out carefully remove the cover.
The battery is obvious and held down by a clip. You just need to flex the clip to remove it. I found that the "fat" end slid out first - again, see picture. After removing the clip, use a toothpick or something to pop the battery out. Put the new one in ("+" up) and flex the clip back into place.
Take a quick look at the gasket - the ridge that runs around the outside of the electronics - for cracks, nicks, etc. I wouldn't remove it if you can help it. If it looks bad you might want to send it to Polar for replacement.
Put the cover back on and put the screws back in. Again the best way to to this is progressively, working diagonally (e.g. left top, right bottom, left bottom, right top, repeat) to insure a nice even seat against the gasket.
Done - redo all your settings and such.
See picture below. Sorry about the quality - I was doing this at work and all I had was my crappy phone camera. Once you have the watch open in front of you it will be very clear, I think.....