There are various coins which allow you to earn rewards/interest, but for this post I am going to focus on Tezos (XTZ). Staking basically means you can earn interest from simply owning coins in a crypto/blockchain.
Tezos uses a proof of stake algorithm (specifically "liquid proof of stake"), which allows for decentralized governance while reducing computing costs when compared to proof of work algorithms.
Tezos staking (AKA "baking") allows anyone with a certain amount of Tezos coins to validate blocks on the Tezos blockchain (a validator is known as a "baker"), and earn rewards based on the size of their stake. Due to the high cost of entry (minimum 1 roll, or 8,000 Tezos at the time of this post) many people choose to delegate their Tezos to a baker. This allows them to earn interest on their Tezos without having to meet the minimum 1 roll requirement. This also works well for those who may meet the minimum requirement, but do not wish to run a computing node. The advantage a baker gets is a higher chance of baking blocks (having more rolls increases your chances of baking a block), and thus a higher chance of earning rewards. When the baker earns their rewards they divvy up the proceeds (minus the baker's service fee) to the delegators based on their delegation size so everyone receives their fair share of the rewards.
Delegation is considered safe because you do not actually move your XTZ coins out of your wallet, nor are they locked up/frozen. You can still use them any time you want. The only thing that happens is your voting rights are delegated to the baker. For the majority of users, delegation is considered the best method because you don't have the costs of maintaining a compute engine, power, cooling, etc.
The easiest method to delegate is to simply hold XTZ in a coinbase wallet. You may also need to opt-in, but in a lot of cases they automatically opt you in if you're eligible to earn rewards/interest. Note that the APY listed on their website is a projected rate. The rate will vary due to how the protocol works (see above).