How do people immigrate to the US when they have no US sponsorers and no lottery visa? ?

If they come without permission, they are invaders.

They are supposed to contact their local American Embassy for the paperwork BEFORE coming here.

There are NO asylum seekers either, unless they are from a communist country and even then they are dubious at best. They are liars.

They may qualify for work visas

They don’t.      

They do not. You have not seen that.

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The number who are sponsored by employers is far greater than the number who can petition for themselves. The US issues about 65K H1B visas annually and after a certain number of years the sponsoring employers can sponsor green cards for those professionals. But there are also untold thousands here who just overstayed tourist and student visas. Why ask anything about formal immigration regards a nation that has no real enforcement of its immigration laws. People just do whatever they want and no one stops them. 

By having a skill, or profession in high demand in the USA. 

They have high level degrees and work skills, a US job offer along with the US employer sponsoring the visa and/or they are investing in US  business and/or talent as in being a well known /highly respected actor sports person etc, someone who has a respected high level talent

Employment visas, visas based on extraordinary talents; visas granted to certain skills, there are many different kinds.