The first part of the process is controlled by the political parties in each state and varies from state to state. Generally, the parties either nominate slates of potential Electors at their state party conventions or they chose them by a vote of the party's central committee. This happens in each state for each party by whatever rules the state party and (sometimes) the national party have for the process. This first part of the process results in each Presidential candidate having their own unique slate of potential Electors. 
Political parties often choose Electors for the slate to recognize their service and dedication to that political party. They may be state elected officials, state party leaders, or people in the state who have a personal or political affiliation with their party's Presidential candidate. (For specific information about how slates of potential Electors are chosen, contact the political parties in each state.)