How does one become a candidate of the Republican party if they have no political past whatsoever? What's the process behind this?
In a general sense, they simply declare that they're running for President, and fill out the appropriate paperwork.
More specifically, there are federal campaign finance forms that have to be filed and you need to get onto the primary ballot in each state. This page from the Federal Election Commission lists everyone who has filed the appropriate paperwork to register as a 2016 presidential candidate.
Each individual who is a candidate for federal office must file an FEC Form 2 within 15 days of becoming a candidate. The candidate may file this form on paper or electronically. Paper filers may choose to send a letter that contains the information required on the FEC Form 2, in lieu of the form itself.
Under the Federal Election Campaign Act of 1971, as amended (the Act), an individual becomes a candidate for federal office when:
- The individual has received contributions aggregating in excess of $5,000 or made expenditures aggregating in excess of $5,000; or
- The individual has given consent to another person to receive contributions or make expenditures on behalf of him or herself and that person has received contributions aggregating in excess of $5,000 or made expenditures aggregating in excess of $5,000 (11 CFR 100.3(a)).
However, you can file even if you haven't reached those requirements. Currently, there are 1663(!) people registered, although a number of those (like Buddy the Cat of the Democratic Party and The Ghost of Christmas Present MMXV of the One Earth Party) are clearly not seriously candidates. (For the record, here are Trump and Clinton.)
Separately, you need to get on the ballot in each state. Each state has their own requirements, which are called ballot access laws.
[P]olitical parties have considerable freedom to determine the methods by which they nominate presidential candidates. In those states that conduct presidential preference primaries, there are usually some statutory candidate filing requirements, but these vary considerably from state to state. In most states that conduct primaries, a candidate may petition for placement on the primary ballot. In some states, elections officials or party leaders select candidates to appear on the ballot; candidates selected in this manner are not usually required to file additional paperwork. In other states, a candidate may have to pay a filing fee (to the state, to the party, or both) in order to have his or her name printed on the ballot.
That page has a table which gives a summary of each state's laws. As three examples:
Arizona: The candidate must file a petition containing at least 500 signatures. Alternatively, the candidate must prove that he or she will appear on the ballot in at least two other states.
Louisiana: The candidate must pay a filing fee of $750, plus "any additional fee imposed by a political party state central committee." Alternatively, a candidate may petition for placement on the primary ballot. This petition must contain at least 6,000 signatures; only voters belonging to the same party as the candidate can sign the petition.
Texas: Ballot access methods vary by party