We had several requests for Signet coins (on Signet, the default signet¹) in the past week. This question is meant as a lightning rod to answer how to go about and where to direct a request for signet coins instead of asking for signet coins here on Bitcoin Stack Exchange.
¹ If you are looking for just any sort of testing environment, rather than coins on the default Signet, check out Is there a sandbox in bitcoin for testing?
Since Signet is centrally controlled, you only option is to get it from a faucet or ask for coins in the bitcoin-signet IRC channel. But depending on what is your goal, there are other great alternatives to signet which are easier to mine or test with.
Testnet has a special rule, which makes it easy to mine in particular circumstances. If there are no blocks found for more than 20 minutes, the difficulty drops and you can easily mine a testnet block with a normal CPU. Obviously your luck depends on if other powerful miners are mining or not. I use this primitive bash miner script to mine and I found 6 blocks in less than 2.5 months.
In many cases you don't need to test on a public blockchain, so why not run a local testnet? It works just like the Bitcoin network, but external connections are disabled and the mining difficulty is set to 0. This allows you to mine as many blocks as you want, making testing faster and easier.