To mine Pi all one has to do is install an app on their mobile phone. The mobile app connects to one or more nodes and checks if transactions have been recorded on the ledger. It also gets the most recent block number and hash value. The app connects to multiple nodes to cross-check this information.
Pi seeks to both avoid the concentration of wealth and reward early miners with a relatively larger share of Pi. This means that people who join the network early get higher Pi mining rewards. These rewards will decrease as the number of people in the network grows.
Right now the Pi server is operating as a faucet to simulate the behavior of the decentralized network as it will function once it is live. During this testnet phase, the Pi team is focussing on improvements in the user experience.
However, all the coins minted by users will migrate to the live net once it launches. In other words, the livenet will pre-mint in its genesis block all account holder balances generated during Phase 1, and continue operating.