iOS: The basic invitations are simple SMS messages. They will be charged as standard outgoing SMS by your carrier (unless sent via iMessage). Naturally, you have other options to bring your friends here. Try sending them a download link via any other messaging service: email, Facebook, WhatsApp, an actual telegram — you name it. The link: https://telegram.org/dl/
Android: Open the app menu (swipe right in chat list) > Invite Friends. Then choose an application via which you would like to send out invitations.
You can give your friends a t.me link with your username so that they can easily find you on Telegram even if they don’t have your phone number.