Is it possible to mine Stellar Lumens and how can I do that?

Actually, it is not possible to mine Stellar Lumens. It is similar to Ripple. 100 billion Stellars were created when the Stellar Network was launched in 2014. Stellar Lumen, XLM, is based on a consensus algorithm. In that case, it is not possible to mine such a digital currency since it has fixed units controlled by the network unlike Bitcoin and other altcoins. When the Stellar Network created the 100 billion Stellars, it distributed 95% of them to individuals, not for profit organizations, and bitcoin holders, while the 5% remained with the organization. This was one of the ways to get new Lumens as they were freely distributed to individuals who had interest in the Lumens.

But is it possible to get new Stellar Lumens, today, without buying from the exchanges and other markets? Yes, it is possible, but only through an inflation policy where new Lumens are generated and added to the current ones at a fixed rate of 1% per year. After the new Lumens are generated, they are distributed to the holders of the digital currency based on a voting process. Still, in that inflation pool of new Lumens, there is a transaction fee of 0.00001 XLM which is charged for every transaction made. The fee, for every transaction operation, is added to the inflation pool for distribution. To qualify for the extra Lumens, you will need to get at least 0.05% of the votes cast.

In short, if you want to earn new Lumens every year, just hold Lumens in your account long enough. You can then wait for the fixed inflation of 1% to kick in and hope to get at least 0.05% of the votes for XLM to be distributed into your account.