What is staking?
In contrast to a proof of work system (like Bitcoin), where everyone tries to solve a riddle to mine a block and get a reward, it's more like a lottery in a proof of stake system (like Cardano).
In this lottery each ADA is like a ticket and everyone who participates can win the lottery, but of course, those with more ADA have more tickets and thus a better chance to win the lottery to “mint” (mine) a slot (block) and get a reward.
To be precise, you don't win the slot but the chance to mint a slot. The one who wins the lottery has to do a tiny bit of work - so, to take the chance, he has to be online in that moment.
This is where the concept of delegation comes into play. A stake pool is online 24/7 on your behalf, so you don't have to be. You can “delegate” your stake (your chances to win the lottery) to a pool.
To be crystal clear: delegating your stake to a pool does not put your ADA at risk. You are not sending your ADA, they are not locked up in a way, there is no minimum and you can still at any time add or remove ADA from your wallet. The worst thing that can happen is that your selected pool does not perform well, make sure to track your pool performance from time to time.
By the way Cardano's proof of stake protocol “Ouroboros” is several thousand times more cost and energy effective than Bitcoins proof of work and it's the first proof of stake protocol, that has mathematically been shown to be provable secure.
Delegate your stake
How does it work?
Delegating your stake will be done within your wallet. It will be as easy as selecting a drop down, like seen in this mockups. You don't need to trust a pool, the rewards are distributed by the protocol, not by the pool. You can stake your ADA with hardware wallets and even with paper wallets.
Very likely, Wallets will help you to select your staking pool, sorting the pools by a new metric called “desirability”. Desirability is composed by: reliability (online when needed?), the pledge (pool's stake), saturation (is it full?), pool costs and margin.
Confirm the delegation with your spending password, a very small fee has to be paid - Again, no ADA will leave your wallet for staking.