The question remains rather unclear about the setting, so let's look at existing drivers and retarders of migration and see which might apply.
Given that we're not forcing people to travel to Mars, we just need to make sure that the idea (note, not the reality) of living on Mars is more attractive than the idea of staying put on Earth.
The factors which make people want to move generally break down into two categories:
Push factors (things that make you want to leave home)
The two most common push factors we see today are economic (a lack of work) and danger - these both come in many forms, and are particularly strong drivers because they often make living in the source country impossible.
Other push factors are things like lack of freedoms (for example, wanting the freedom to practice their religion or things which don't pose a direct threat to life, but make life in the source country intolerable).
Pull factors (things that make you want to arrive somewhere else)
These are often economic too, but unlike the known realities of life in the source country, are often based at least partly on promises and hopes. People will move to a city because they believe life will be better there, regardless of whether or not that is true (a famous example of this being English migration to London).
Other pull factors can be climatic (think people retiring to the Carribean), idealogical (most famously Cold War defectors), lifestyle based, or any other reason people would want to live somewhere else.
These drivers are then set against the factors that make people want to stay:
Factors that make you want to stay where you are
Familiarity and family/friends are the big ones here. It's a big deal leaving everyone you've ever known behind, and that's doubly true when moving to a different planet entirely. In general, anything which makes you happy with your life in the source country will make you less likely to want to move.
Factors that make you not want to go to the destination country
For frontier countries, this normally means danger, but other things like hardship (or indeed any of the previously mentioned factors) also apply.
Difficulties and costs of migration
If it's difficult, costly or dangerous to actually make the journey, fewer people will make it. This has been true right the way through history, and is still true in the present day (think of the migrants and refugees attempting to cross the Mediterranean - many of them want to make it Europe, but lack the ability to get there).
Applicable factors for Mars
As with all other migration, the biggest drivers will be opportunity (on Mars) and danger (at home). If you can ensure that enough Mars colonists do well for themselves then people will want to go there, and it can be pretty safely assumed that there will still be refugees on Earth who would jump at the chance to go literally anywhere else.
This isn't as simple as it sounds though - in order to get any real numbers of people you'll need to ensure that people can live on Mars, which really means that you'll need to have built (or organised) your colony before people will move in - wealth means nothing if you can't spend it, and opportunities mean nothing if you're not alive to make use of them.
One unusual driver is the excitement and adventure of living on Mars - Mars One received more than 200,000 applicants, even with no possibility of return.
Of course, being on a different planet is a formidable challenge for a colony. Given that regular people don't have the resources to get to Mars on their own, a prerequisite for migration will be an already existing space transport service to get them there. Basic economics tells us that demand and price are inversely correlated, so for maximum numbers of migrants it should be as cheap as possible - financing options such as working one's passage will also help.
Space travel is also risky, so you'd want to make your service as safe as possible too - again easier said than done.
The reality is that, as long as you make Mars colonisation possible, motivating people to move there won't be a problem.