There are multiple ways of sharing your wallet address. The most standard option is just to copy and to paste your wallet address, however, some people make mistakes while copying and pasting. Therefore every XEM wallet has it's own QR code and a QR code scanner, so you can’t make any mistakes when sending or receiving money.
You can save other’s addresses in the Address Book. It is a list of the contact names and their matching addresses, so when you need to send some XEM to one of your contacts, you can simply use the address from the Address Book.