affectionate, friendly
reassuring
congratulatory
comforting (AmE)

give sb/sth
He gave the dog a pat.

pat on
He gave her a reassuring pat on the shoulder.

gently, lightly
affectionately
awkwardly (esp. AmE)
I threw my arms around him and he awkwardly patted my back.

on
He patted her gently on the shoulder.

Pat is used with these nouns as the object:
arm, back, belly, cheek, head, knee, mane, pocket, stomach, tummy

Pat is used with these nouns:
answer