Staking is the process of delegating ADA that is in your wallet to a stake server. The cardano blockchain algorithm Ouroboros is a proof-of-stake algorithm, which means that it chooses which block producing network node is the one to produce a new block containing transaction information and other metadata based on the amount of total active stake this block producing network node, also called stake server, has. Each ADA (or its currency subunit Lovelace, actually) acts as a raffle ticket for this selection process. Every few slots (one slot is one second and a block is produced every ~ 20 slots) one such ticket is drawn by the algorithm, and the holder of the ticket wins the prize to produce a block and to collect the associated rewards. However, only stake servers can actually produce and write blocks to the blockchain, so how can ADA holders who do not run their own staking servers be included in this process? They can delegate their ADA to a stake server to do that for them (so ADA is "pooled", stake servers are also called stake pools for that reason) and the stake server shares the rewards with the delegators in turn. So staking gives all ADA holders the chance to participate in this selection process and to collect some of the rewards if a block is sucessfully produced. Staking is primarily about including every ADA holder to secure the blockchain, and the rewards are an incentive to do that as the staking rewards increase the total amount of ADA in your wallet by 4-5% per year. The chance of being selected increases with the amount of ADA delegated to a certain pool, so pool operators are happy about any ADA delegated to their pool.
Staking is without any risk for you as the ADA in your wallet never leave your wallet and staking ADA works without locking them up so you can use the ADA in your wallet any time. The reward mechanisms and the reward payouts are automatically handeled by the protocol without the intereference of anyone, and it just works. There minimum amount of ADA required for staking is low (10 ADA), so it is highly recommended to stake any ADA you hold. It is recommended to use native wallet apps, and although most of the major crypto exchanges offer staking as well, it is generally not recommended to leave your funds on exchanges. The exchanges ultimately control your funds, and if anything happens to the exchange, you might lose access to your funds: Not your keys - not your coins
Exchanges usually also keep some of the staking rewards and they are the big players, so if you delegate your ADA to them, you are not supporting decentralization, one of the core principles of cryptocurrencies in general. So there are many benefits with delegating to a small pool, on top of that you can also support other good causes by choosing a charitable pool like ATFF pool who donates some of the rewards they receive to charities.
So how can you do that? It is actually pretty simple, you install a wallet app, transfer your funds to this wallet and choose the stake pool you want to support right from your wallet app.
First of all you need a wallet app so you can delegate your ADA to the staking pool you want to support. Cardano currently supports two native wallet apps, Yoroi and Daedalus. Yoroi is a lightweight wallet app that runs on mobile or as a browser extension, Daedalus is a full node and can be installed on Windows, Mac or Linux. It doesn't really matter which one you pick in terms of staking. With a full node you also support the network, but you have to install it and it synchronizes with the blockchain, which can take some time when running it the first time. Always download crypto software from official sources! https://yoroi-wallet.com/ and https://daedaluswallet.io/.
Important concept: The term 'wallet (app)' is actually a misleading term because it actually doesn't contain any coins such like a conventional wallet does. It is actually an interface to the blockchain that sits on network nodes all over the world and the app manages and uses private and public keys to make transactions on the blockchain. All balances, the transaction history and other data are stored on the blockchain, and many of the interactions with the protocol, such as delegating to a stake pool, are handeled through transactions as well.
Now what is this, a wallet inside my wallet app? The wallet is basically a collection of addresses and keys to these addresses, and the key to the wallet is the wallet seed phrase. Anyone who has access to the seed phrase has access to the contents of your wallet and can use a wallet app on a different device to do that (because as we just said, a wallet app is only an interface to the blockchain). So it is most important to save your wallet phrase in a secure offline location and to use a safe and unique spending password.
You need the spending password for every transaction and if anyone gains access to the device on which your wallet app is installed, can transfer funds using it. The wallet seed phrase is your backup key to restore the whole wallet if your device dies or is lost.
Please choose an approach to save your wallet seed phrase that is the right one for you and adequate for the amount of ADA you are holding. It can range from writing it on a piece of paper and storing it in a secure location, to engraving it on a steel plate and locking it up in a safe deposit box, and anything in between.
To repeat this, if you lose access to your wallet app and also lose your wallet seed phrase, you lose access to the wallet's contents (your funds), and nobody will ever be able to retrieve it for you, so take care not to lose it, and to not let anyone have access to it who shouldn't. Please also consider using a hardware wallet such as Ledger or Trezor which add another security layer for Yoroi or Daedalus, the same rules for your wallet seed phrase apply though, and it might be overkill for smaller amounts.
Once you have created a wallet, you can start transferring ADA to it. In Yoroi, go to the receive tab, click generate new address and copy that address or use one of the existing internal addresses. The receive addresses can be shared with others or a crypto exchange to send you ADA. Alternatively you can also use the QR code. Sending ADA works the same way, you need the address to send ADA to, enter the amount of ADA to be transferred and confirm the transaction with your spending password. Don't ever type wallet addresses by hand, use copy+paste or the QR code and triple check whether the correct address is used, because if you send your ADA to an address you don't control, they are gone! If you want to transfer large amounts you can do a test transaction with a few ADA first and see if they come through, then repeat with the bigger rest. You can also check the balance of a single address or your whole wallet by looking it up on the blockchain using the Cardano Explorer.
Now let's go to the actual staking process. In the delegation center of your wallet app you can choose from currently more than 2500 stake pools. Now it is hard to decide which pool to use, the easiest is to stake with ATFF, we have reliable servers and lowest fees possible, we donate some of our own rewards to volunteer fire departments and we happily welcome each new delegator. We have a low total stake currently so we don't mint blocks very often, but this does not matter very much from your perspective: Although you get rewards less often, the reward amount is higher and it averages out at around 4-5% ROI per year in any case. For example, a pool with a total stake of 1 million ADA mints blocks regularly, but if the pool is oversaturated, the rewards suffer, so any pool above 64 Mio ADA should be avoided. Reliably minting the blocks a pool is assigned to is most important, nothing is worse than missing blocks because the server is down or because the software is not up to date. Low fees are important too, there is a minimum base fee of 340 ADA a pool operator receives, and most pools use this minimum fee anyways, so I would choose one with a base fee of no more than 340 ADA. Then, the pool can also define a certain percentage of fees they get, and a low percentage margin fee is important, anything below 5% can be considered reasonable. And there are other factors too, as mentioned there are pools like ours that support other good causes and there is an alliance of mission driven pools (https://missiondrivenpools.org/) and you can't go wrong with picking one of them.
When you have chosen the stake pool you want to stake with, go to the Delegation List tab in Yoroi, search for the pool using the ticker ATFF and click delegate. A window pops up where you enter your spending password and click delegate to confirm. The total amount in your wallet is shown in the amount field, because split delegation is not supported yet and you always delegat all your ADA to a single pool.
By confirming the transaction you deposit 2 ADA that you get back when you unstake your funds eventually, and this transaction costs around 0.17 ADA in transaction fees. Apart from that, staking is free, and you can use the ADA in your wallet any time and for example transfer funds from your wallet somewhere else, so they are not locked by staking. If you add ADA to your wallet, the additional amounts are automatically staked as well, the same is true for the staking rewards you receive. Rewards are automatically paid out at the end of every epoch (one epoch equals 5 days) in which a block is minted, but the payout is delayed for three epochs, so you have to wait for 15-20 days before receiving the first reward payments and only if the pool generates a block during that epoch.