In Cardano, time is segmented into 5 day epochs and 1 second slots.
As users publish transactions on the network, pools distribute the transactions to their peers and store valid transactions locally in a queue, known as the mempool.
In each slot, one or more validators (pools) may be selected to forge a block. That block will contain transactions from the mempool, up to max block size.
Validators are able to independently check if they are elected as the slot leader. From the Ourobouros Praos paper:
only a slot leader is aware that it is indeed a leader for a given slot; this assignment is unknown to all the other stakeholders—including other slot leaders of the same slot—until the other stakeholders receive a valid block from this slot leader
Blocks are signed by a validator with their operational key and includes the validator's operational certificate. The certificate is composed of the public portion of the operational key, certificate issue number, beginning KES period, and a cold key signature as defined in the ledger spec.
Once the new block is distributed to the network, each other validator can verify that the new block is valid, and that the publisher was eligible to forge a block in that slot.
All of this happens automatically as part of the
cardano-node software. Operators only need to update their certificate periodically.
The proof of this distributed random selection process is a bit much for this answer, as is the proof for how the network selects a longest chain and handles soft forks, but worth reading up on if you're interested in this topic!