If this first contact happens when a unit from one civilization reaches the borders of the other, the 'discovered' civilization is given the option to reveal one of its nearby cities to the 'discovering' one. The introductory movie for the respective leader is then played, after which you are given the options to briefly make introductory interactions. This is done when a unit of yours enters within visibility range of the other civilization's borders or units, or vice versa.
In order to establish relations with any major or minor civilization you have to first 'meet' them. 8 Diplomatic Victory and the World Congress.
