The money to pay for all costs may come from different sources. Since the costs for building a settlement on Mars are astronomically high, a global funding seems to be the most promising approach. The first human mission to Mars may be estimated with about 10 billion USD.
Funding by Government
National space agencies, like NASA, have several responsibilities. They are busy enough with orbital and scientific tasks. Extraterrestrial colonization is usually not in scope.
There are very few super-rich people on Earth, whose money would suffice for a first step of Martian colonization.
Generating money from global media events is the plan of Mars One. They want to generate 6 billion USD during a period of 10 years. Compared with the Olympic games, which generated about 3 billion USD within two weeks, this sounds promising.
Donations by many people around the world may result in vast amounts of money. But most people are sceptic about the outcome of the project. A person may donate 100 USD to support the project, but can not be sure that this donation really leads to the wanted landing on Mars. If the financing is not sufficient, the project will fail. So, the donor has spent the money for nothing.
What if the success could be guaranteed? How much would the same donor pay, if he can be absolutely sure that the money will have the wanted effect, that the colonization comes true? Would he pay ten times as much, e.g. 1000 USD? The following crowdfunding model could provide such a guaranty.
Secured Donations with Guaranty
At the beginning of the project the donor signs a contract with the colonizing organization, in which he obligates himself to pay a certain amount, e.g. 1000 USD, as soon as the colony on Mars is established and the settlers have arrived there. If the project succeeds, the donor must pay. If the project fails, the donor does not need to pay.
This funding model can be compared with buying a car with a deferred payment (say 6 month) and a warranty of 6 month. When the car is still fine after the 6 months have elapsed, you have to pay it, else you give the car back and don't pay.
For funding a Martian colonization project the model will include many contracts with donors from all around the world, which sums up to a large amount. If the sum is published on a daily basis, everyone can watch how far the financial costs are covered. Media companies may serve as very potent donors, if they get the rights to broadcast the live events on TV according to the amount of their donations. Sooner or later the sum covers the whole project. This is the moment the project can start. Until then, no money at all is really available, but the prospect of a success becomes palpable, at least from the financial aspect. Now the organization must convince potential investors that they are technically able to do the colonization. The investors give the real money and the rockets and all the other stuff can be made. The colony is built, the settlers go to Mars. Finally, the investors get a return of their investment from the contracts of the donors, but only if the project succeeds. The donors give the money, but the investors take the risk. Surely, the investors will carefully supervise the organization to protect their investment.
The deferred payment contracts are only one possibility. An alternative is the setup of an interest-bearing escrow deposit or a blocked account. Finally, depending on the outcome of the project, the stored money goes back to the donors or to the investors.
Corporate and institutional Investors
Investment is a question of supply and demand. If there is significant demand for a martian settlement as a living space, then there can be investment, return on investment, speculation and all the standard items of investment. If a martian settlement can provide a reasonable business plan, with provable growth potential, and in particular a period of exponential growth, then it will attract corporate investment, that can be considered as the sum of the interest of any number of mid-sized investors. The question then becomes how much money would interested people be willing to pay to move to Mars, and how much might they pay to stay there. How much can costs be reduced by government involvement in research and infrastructure costs, and can the voting public be convinced to support such investments? An important point to make would be the jobs created on Earth by a martian settlement. After all, most of the goods and services would come from Earth for quite some time.