I haven't seen any how to's on replacing the battery in a polar HRM watch. This is how I changed the battery in my HRM, yours may look different on the inside. It will take around 5-10 minutes depending on how fast you work.
Mine uses a CR2032 battery that cost $3.99 from Walgreens
Here's my HRM waiting for the battery replacement
I used a #0 Phillips head screwdriver to remove the 4 screws on the back cover, when you remove the cover, this is what you will see. There is a very small spring that is just setting there, make sure it doesn't fall onto the floor.
Now, carefully pry the innards out of it, they are just setting in there and will look like this when they are removed.
Around the outside edges are a bunch of little snaps. Carefully pry them up to separate the cage thingy from the rest of the electronics. I used a very small flathead screwdriver to separate the pieces. Keep track of the direction that they came apart so you don't put it back together wrong
Next carefully slide the cage section apart, this will allow you get access to the battery to easily remove it. Pay attention to which side is positive and which is negative.
Now reassemble in the opposite order you took it apart.