If I mint some tokens and want to list them on an exchange somewhere so people can buy them and trade them like other tokens out there, how do I do that?
Has anyone on here successfully listed your tokens anywhere yet for others to purchase them, if so what is your token and where can it be purchased or acquired?
Just minting tokens does not provide the ability to list them on exchanges. The only option to be able to list a token for sell without the approval of the exchange would be a DEX, like UNISWAP. But Cardano does not have a DEX yet for swapping ADA for other Native Assets at this time. You could setup a payment gateway to sell your tokens on your own website, but depending on the laws where that token sale happened could be considered a security. Or based on the statements you use in your marketing to sell it. I would recommend looking into the laws where you want to launch token and it’s purpose before attempting to sell them. Airdrops and other distribution methods have different rules depending location also. Best wishes, don’t give up on your dream 
just DYOR.
I am pretty sure your post has people thinking now of different ways to create a coin and do something with it. I’m looking forward to seeing what the community comes up with here! 
make your own site for selling
Take a look at the NFT DAO project that is in need of your votes for Catalyst 3 Funding.
https://cardano.ideascale.com/a/dtd/Comprehensive-NFT-Framework-Collab/334521-48088
You would need to trade the native token on a DEX. Problem is that there is no DEX for the Cardano ecosystem yet, as @BooneBergsma said.
I’m currently working on a DEX that will allow users to trade Cardano native tokens. You can find more info on the proposal I put on #project-catalyst
https://cardano.ideascale.com/a/dtd/Cardax-DEX-on-Cardano/342252-48088