One of Monero's philosophies is to maintain egalitarian mining, so that everyone can have the possibility to mine. To achieve this, Monero uses a particular algorithm ideated and developed by members of the Monero community: RandomX. This PoW algorithm is ASIC resistant, which means it's impossible to build specialized hardware to mine Monero. Miners must use consumer-grade hardware and compete fairly.
Monero can be mined by both CPUs and GPUs, but the former is much more efficient.
Miners can decide if they prefer to solo mine or to mine in a pool. Each method has its benefits and drawbacks, but the Monero Project encourages individuals to solo mine using the Monero software (GUI and CLI), as this type of independent mining is the most effective way to increase the robustness of the Monero network. Mining using P2Pool is also encouraged.
Pro and cons of solo and pool mining:
If you need help choosing a pool or you just want more information about them, use:
P2Pool is a clever new way of mining Monero, which allows miners to receive the frequent payouts offered by pools without needing to trust a centralized pool. P2Pool is a Peer-To-Peer mining pool that gives miners full control over their Monero node and what it mines. More details in the announcement post.
P2Pool is a sidechain to Monero, and P2Pool blocks are potentially Monero blocks. Each miner submits block templates that include payouts to all of the miners that are mining at the same time (those that currently have shares in the PPLNS window). High quality block templates are added to the P2Pool blockchain as blocks; these count as "shares" for the miner who found them.
More information and details on the GitHub repository of the project: github.com/SChernykh/p2pool
Monero can be mined on both CPUs and GPUs, but the latter is much less efficient than the former. You can get an idea of how your hardware performs compared to others, using monerobanchmarks (some results might be out of date).
There are several options when it comes to mining software. As already said, to solo mine, the CLI or GUI wallets can be used (CPU only). If you want to mine to a pool or mine with a GPU, you'll need dedicated software. Miners supporting Monero: