This is a bit of a general question so hard to answer in detail.
But the basic mechanism for self sovereignty is the private key. So each user would have their own private key, and use that to publish information onto the chain, which other users cannot fake.
If we're talking about end users, this would probably be managed via a mobile app acting as a lightweight (SPV) client on the blockchain, rather than them running a full node.
Users can also use their private key to prove (off-chain) that they own a particular identity which has on-chain attestations from trusted parties (banks, governments, etc...)
