Get Signet coins
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.
Alternative testnets
Testnet
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.
Regtest
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.