how can one qualify for the first tournament?
Qualification is based on UEFA coefficients of the member associations.
UEFA Champions League
The number of teams that each association enters into the UEFA Champions League is based upon the UEFA coefficients of the member associations. 
when did liverpool f.c. started its first international tournament? 1964 what tournament was it? They have won many, including UEFA Champions League, the UEFA Super Cup, and the FIFA Club World Cup.
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UEFA Champions League [SEP] Qualification
The UEFA Champions League begins with a double round-robin group stage of 32 teams, which since the 2009–10 season is preceded by two qualification 'streams' for teams that do not receive direct entry to the tournament proper. The two streams are divided between teams qualified by virtue of being league champions, and those qualified by virtue of finishing 2nd–4th in their national championship. The number of teams that each association enters into the UEFA Champions League is based upon the UEFA coefficients of the member associations. These coefficients are generated by the results of clubs representing each association during the previous five Champions League and UEFA Cup/Europa League seasons.