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The Collaborative International Dictionary
Friending

Friend \Friend\, v. t. [imp. & p. p. Friended; p. pr. & vb. n. Friending.] To act as the friend of; to favor; to countenance; to befriend. [Obs.]

Fortune friends the bold.
--Spenser.

Friending

Friending \Friend"ing\, n. Friendliness. [Obs.]
--Shak.

Wiktionary
friending

n. (context obsolete English) sentiment of friendship vb. (present participle of friend English)

Wikipedia
Friending

Friending is the act of adding someone to a list of "friends" on a social networking service. The notion does not necessarily involve the concept of friendship. It is also distinct from the idea of a " fan" — as employed on the WWW sites of businesses, bands, artists, and others — since it is more than a one-way relationship. A "fan" only receives things. A "friend" can communicate back to the person friending. The act of "friending" someone usually grants that person special privileges (on the service) with respect to oneself. On Facebook, for example, one's "friends" have the privilege of viewing and posting to one's "wall".

The first scholarly definition and examination of friending and defriending (the act of removing someone from one's friend list) was David Fono and Kate Raynes-Goldie's "Hyperfriendship and beyond: Friends and Social Norms on LiveJournal" from 2005, which identified the use of the term as both a noun and a verb by users of early social network site and blogging platform LiveJournal, which was originally launched in 1999.