The newly elected (incoming 2012) House of Representatives will count the Electoral College votes on January 6th. These new members of Congress will be sworn in 3 days earlier on January 3rd.
If there is an Electoral College tie, the House of Representatives will elect the President.
Each State will get ONE VOTE in the House of Representatives. The House members from each State must agree on who to give their vote to from the 3 candidates who received the most electoral votes. So, if an Electoral College voter in any State decided to vote for someone other than Biden or Trump ("faithless elector"), that person could also be an option for the House members. Thus, in this example, someone could become President without ever being on the November ballot.
Some States may have equal numbers of Democrats and Republicans in the House of Representatives, and those House members will have to choose whether to follow their party or, follow the wishes of their State.
The House vote for President is over when a candidate gets 26 votes (majority). If a delegation is split, that State might not cast a vote. The winner of the Presidency must get 26 votes. It is possible that due to ties in multiple States, multiple votes would not be cast. The hope is, however, that democracy will prevail and a President will be selected.
If there is a tie in the Electoral College, the Senate will select the Vice-President. Each Senator gets one vote, and can choose from the top 2 candidates who receive votes from the Electoral College. The candidate who gets 51 votes (majority) will be the Vice-President on January 20th. (Probably Pence if Republicans control Senate.)
If the House of Representatives cannot come up with a winner by January 20th, then whomever the Senate elects as Vice-President becomes President until the House can pick a President.
If the Senate is also unable to reach a decision by January 20th, then the Speaker of the House becomes the temporary President. Therefore, Nancy Pelosi could temporarily become President.
If Nancy Pelosi does not want the job, which is possible, then Chuck Grassley, the President pro-tem (President of the Senate when the Vice-President is not there) would become President until the House selects the President. Pelosi may turn the temporary position down because the second he becomes interim President, the House of Representatives would have to pick a new Speaker, and upon his return, he would be a "regular" member of the Congress. He would no longer be Speaker of the House, if he were to take the job as President.
The Electoral College has nearly always produced a winner--so far. While it has not always picked a winner, it usually gets something on paper. Congress will only have 14 days to pick a President, provided the Supreme Court does not have to get involved to settle disputes at the State level...
The Constitution and Federal Election Laws cover many different possible scenarios. However, many aspects of a tie in the Electoral College have not been taken into account and could provide for some interesting results.