Using ADA is as simple as handling other crypto currencies. You have to install a digital wallet. Later you will transfer your traded ADA to that wallet. There is a choice between two wallet products, one is Daedalus from IOHK and the other is Yoroi from Emurgo.
Daedalus is only available for PCs while Yoroi is also available for smart phones in their respective app stores. Daedalus is running a full copy of the blockchain on your computer (and it takes a while to synch) while Yoroi uses an online copy. For PCs Yoroi has been implemented as a browser plugin.
Please note that there's no Daedalus app. If you find one in your app store it is a scam.
The next step is registering with an exchange. After you have identified yourself with the exchange you can transfer your fiat money to the exchange and trade ADA for it. Now you have some amount of ADA in the wallet of your exchange. It is important to transfer that amount to your own wallet. Otherwise you cannot get any rewards for your stake.
After withdrawing your ADA from your exchange and receiving it on your own wallet, i.e. you'll have it in your Daedalus or Yoroi wallet, you can delegate to a staking pool. You can just enter the delegation list and choose ADAAT as ticker to delegate. Once your ADA has been delegated, any further increase or decrease of the amount in your wallet will automatically adopt your stake in your choosen pool.
Rewards are then automatically transfered to your wallet and added to your stake.
Please note that your stake in ADA will only start with the next epoch (epochs start every 5 days) and that rewards payment will be done 2 epochs after blocks have been minted.
If you have questions left, please don't hesitate to email us: askJoe@adapool.at