You can't send friend requests on Steam until you buy a game or add funds to your Steam Wallet. New accounts are locked into a limited state until a small amount of money is spent. If you want to add friends before buying anything, ask your friends to send you an invite link.

If you encounter issues when creating an account while using a web browser, please try creating a Steam account using the Steam client/application: Download and run the installer for Steam from http://store.steampowered.com/about.

How can I gain access to all Steam features? To access all features of Steam, simply do any of the following on your Steam account: purchase a game from the Steam store (It cannot be a gift for another account), redeem a Steam gift, or complete a microtransaction.

Limited accounts are restricted from adding friends. However, you can still accept friend invites from other non-limited users. For example, if a friend is already on Steam and has spent $5 USD or more from the Steam store, they will be able to add you as a friend from your Steam Community profile.