The Spanish phrase "buscar pareja" is generally used to refer to dating. For example, "buscar pareja en línea" would refer to the act of online dating.
The phrase literally translates as "looking for a partner," according to SpanishDict.com. The Spanish verb "buscar" means "to look for," and "pareja" can be used to refer to mean a couple or pair, a partner, or a significant other.
The process of dating involves a pair going out with each other as part of their search for a significant other. The actual act of going out with someone translates into Spanish as "saliendo con." It comes from the Spanish verb "salir," meaning to go out, and the word "con," meaning with.