LMIA Owner Operator: To get this you need to EITHER - buy out the majority share (50.1% or more) in an existing business in Canada OR set one up from scratch/expand/transplant your existing business into Canada. There is no capital investment requirement and no specific amount of cash you have to show you have access to but if you're going to buy a business it's quite likely that you have a pool of cash you can tap into.
If you're a sole proprietor/freelancer then you may not need any substantial capital investments up front for your business (for instance, I am a freelance sound engineer. I need my ears and the things I know about sound to run my business and that's it). Therefore, your business plan is going to have to be a work of art to get an LMIA.
You submit a detailed business plan, your LMIA Application paperwork and the LMIA application fee (currently $1000) and then an officer from ESDC assesses your application. They will likely invite you in for an interview to discuss your business proposal and you really had better know your business and business plan inside and out, upside down and back to front.
You will have to demonstrate that you will be providing value (financially, culturally and in terms of the wider Jobs Market) to Canada and Canadian life. There is a stipulation that you need to hire at least 1 Canadian or Permanent Resident. You are exempt from the advertising requirements of most LMIA applications as you are seeking to hire yourself to do a job that only you can do.
If you are granted the LMIA you then apply for a Temporary Work Permit as per any foreign worker as you are effectively hiring yourself as your first employee.
That's all there is to it. That doesn't mean that it's an easy way in. The benchmarks for "Canadian Benefit" are pretty high and rigorously enforced.
A lot of people on this thread seem to be confusing LMIA-OO with other Entrepreneur streams. This is NOT a direct route to PR; this is a route to a work permit which will give you Canadian Work Experience that you can transfer to EE under the Canadian Experience Class.
There is another similar route that is likely even more difficult to get: LMIA Exempt TWP. In order to get this one you have to demonstrate that your working in Canada is of great value to Canada, more so even than under the LMIA-OO route. Refer to International Mobility Program Section 205 Exemption Code C11 for more details.
Just a quick note: I am not a legal consultant, I am not legally authorised to offer legal advice so don't ask, also, I will not be handing out my phone number so we can WhatsApp offline with anyone so again, don't ask.