The most used wallet is the mobile wallet, running as an app on your smartphone, the wallet can store the private keys for your Bitcoin addresses and enable you to pay for things directly with your phone.
Examples of mobile wallet include android based Bitcoin Wallet, Mycelium, Xapo and Blockchain.
These keep your Bitcoin keys encrypted on your phone and backed up on a web-base server.
You can choose your wallet from app store on your phone and easily download it.
You will supplied a series of words, usually 12 or 24 words, these are called private keys, it is imperative that you physical write this words down and store them safely in a safe box or anywhere else that you feel is a secure place. You will need some of this words, that will be randomly chosen by you digital wallet, to make a Bitcoin transaction. Don’t worry, it will not be the whole series of words, usually 4 only.
It is advisable NOT to store these word in your phone memory, if you unfortunately lose or destroy your phone, these important words will be lost, possibly resulting in the loss of your Bitcoins.