How are members chosen by the electoral college until we get a President?

The laws in each state (and for this purpose, state includes the District of Columbia but not the other territories) are different. (Article II, Section 1, clause 2 of the Constitution allows each state to pick its own method of selecting electors.) Generally speaking, for the established parties (i.e. those that got more than 1% of the vote in the last election cycle), the candidates for electors are chosen either by the state committee of that party (in most states, individuals run as part of the primary election to serve on the local party committees which then choose members for the next higher committee up until you get to the state committee) or by the state convention of the party (basically the top tier of the caucus system in states that use local caucus as part of the delegate selection process for the national convention). In either case, these people tend to be activists who are well known to the party leadership and are trusted to support the national ticket if they win the general election in that state. For new parties, the people circulating the petition to get the party on the ballot get to choose the proposed electors.

In the general election, (though not listed on the ballot in most states), each party's nominees for elector are part of the ticket of the candidates running for president and vice-president. All of the states use a first past the post system in which the ticket that gets the most votes (not necessarily a majority of the votes) wins. In all but two states, winning state-wide means that all of that party's nominees for electors are chosen as the state electors. In two states (Maine and Nebraska), the state-wide winner gets it's two candidates for at-large elector chosen. In addition, the winner in each Congressional District gets it's candidate for district elector chosen.


In each state, the chosen electors meet on the first Monday after the Second Wednesday in December. (U.S. Code, Title 2, Section 7.) At that time, they cast one vote for President and one vote for Vice-President. Some states have laws that, at least on paper, bind those electors to vote for their party's candidates, but the validity of those laws have never been resolved. After those votes are tallied, the results are announced and a certified copy of the tally is sent to Congress.


On January 6, a joint session of Congress meets to count the tallies sent in by the individual states. (U.S. Code, Title 2, Section 15.) At that time, if there is some irregularity in a given state's vote, a challenge can be made by a representative or Senator. If a challenge is made, each house votes separately whether to grant the challenge or to accept the vote as certified by the state. If either house rejects the challenge, the vote as certified by the state is accepted (which is what always happens). Once all challenges have been resolved, the votes are tallied. If an eligible candidate has 270 electoral votes, that person is certified as the president-elect (or vice-president) elect.


If no candidate has 270 electoral votes (that number is based on the current number of electoral votes, if the total number of electoral votes changes in the future, the new number would be whatever number it takes to have a majority), then it goes to Congress to pick the winner (under the Twelfth Amendment). The House, voting by state, would choose between the top three candidates (the text of the Constitution does permit the House to limit it to two candidates which would be likely in the case of a 269-269 tie) for president with it taking a majority of the states to be elected. If no candidate for Vice-President received 270 votes, the Senate would choose between the top two candidates with each Senator having one vote.

The States' Party leaders register specific persons to be their Electoral College representatives.
To prevent a "Write in" candidate from winning the voter would have to write in ALL the names and addresses of the Electoral College for that individual, not the candidates name.
Conveniently, No Ballot has enough room.

For a Tie: the election for President is decided in the House of Representatives,

Differentlt

Members of what? The question makes no sense.

If no candidate wins a majority of electoral votes, then the House of Representatives selects the President from the top three candidates.

This is all spelled out in the Constitution which, apparently, is no longer taught in school.

Follow the money.