Mint beer and experimenting with mint and beer does not sound interesting to me, but if it did, I would start by adding a few drops of mint extract to some commercial beer or homebrew that is ready to drink. A bit in an American wheat or a blonde would probably be my approach, unless you're going after the Girl Scouts Thin Mint flavor.
If experimenting with extract in beer that is ready to drink turned out to be any good, then I would crush some mint leaves into some vodka, soak for a few hours/days, then add the strained vodka to the bottling bucket or keg. I have no experience in this, but that would be my approach. I use mint for other drinks and food. I often make strawberry mint soda, mint limeade, and add mint to margaritas. Mint beer is just something I wouldn't want to try. Maybe in a strawberry wheat beer I've made, but that's it.
Edit: Maybe trying a recipe with some minty hops like perle would help accentuate that flavor and aroma. Mint is something I like more to accentuate the flavor profile, not contrast it, if that makes any sense. But that's my preference. I know some people really like mint in their coffee and chocolate. Not me. Mint is a fresh flavor. I pair it with other fresh tasting ingredients.