To take tasks you must link at least one social account. The market only shows tasks for networks where you have an account.
Adding an account asks for the network, username and profile link. You can also set the account's country, language and gender — targeted tasks match on this.
The verification method depends on the network (a like, a follow, a channel status). Real verification works for Telegram; on other networks the account is currently activated directly and verification arrives in a later stage.