Google 'removing acoustic guitar bridge' or things like that and you'll come across lots of tutorials, advice, etc.
I like to carefully and slowly score the edge where the bridge meets the guitar all the way around several times, being careful to only touch the glue and not the wood. After scoring, I then cut a piece of cardstock to fit around the bridge very closely (this will protect the finish below the card somewhat).
Next, I put a hot iron on the bridge itself. You can buy these, but I just use a household iron with a medium heat setting and no water in the tank (you don't want any steam in this process). As long as I keep the heat around 250 degrees max, I find the wood below won't burn.
After about 10 minutes of heat and careful monitoring, I slowly work my way under the edges of the bridge with a very thin putty knife. Again you can buy these, but I have an art putty knife whose edge I've razored - works well. Slow, careful repetition and the bridge usually pops off after a few minutes. I occasionally reapply heat if its a tough job.
This is finicky stuff though, and lots can go wrong, so I'm always prepared for the possibility that I'll be refinishing the entire top if something goes haywire. I have to say though, that after repairing many bridges this way, I've only crapped the bed once and had to redo a guy's entire top. I don't ever want to do that again!
Once the bridge is off, if there is any damage to the finish around the edges of where the bridge was, it can often be covered by making the new bridge a couple of mm larger than the old one. When replaced, the new bridge will hide the old marks...