Background
On the beacon chain, each validator needs to specify a withdrawal address on the execution layer by signing a cryptographic message. After that, all the ETH held by the validator will be under the control of the withdrawal address: ETH leaving the consensus layer will go to this address, and it is also able to force the validator to exit. The withdrawal address can also be a contract or a smart wallet. It cannot be changed once set.
It is always possible for the validator to be run by a different entity, since the validator key does not have the power to take the funds. It only controls the validator's performance and any MEV.
Given these features, there are multiple ways to set up a validator. OG solo stakers, and many whales --- for example The DAO Fund, set the withdrawal address to their wallet. It has many advantages: it is simple, has no slippage, does not introduce a smart contract attack surface, and keeps the entity's validator segregated from any other's. The tradeoff is inflexibility: the validator cannot be moved from the original wallet or used in DeFi. This is not necessarily a problem for these entites.
Another popular option is staking using a centralized exchange such as Binance, Coinbase, or Kraken. This is convenient, secure, accessible with less than 32 ETH and can also come with some legal guarantees, but the users are not in control of their funds and it does not compose with DeFi.
Coming back onchain, a common option is liquid staking tokens, or LSTs. These protocols represent user's staked ETH as fungible tokens that can be held in wallets or used in DeFi and secondary markets. Validators might be run by permissioned entities like in the Lido CM, or access might be permissionless like in Rocketpool or Lido CSM. All current LST designs (or quasi-LST designs like StakeWise V3) use a set of oracles to determine the amounts owed by the protocol to users and validator operators. Since Ethereum itself is still evolving, privileged keys are also able to upgrade most of the protocol, ultimately making those not trustless. Despite this, they are great products and it is fine to use them! However, as a matter of curiosity, one may want to know if there are alternative, trustless designs.