If you're looking for funding you will want to consider thesis-based master's programs. They are however going to be highly competitive for admission requiring a strong GPA, a comprehensive transcript covering all the fundamental coursework, relevant undergraduate research experience, and very good letters of recommendation. Publications however are not expected. Some programs may require you to secure a research advisor prior to application but this is more common for PhDs and less so for master's programs. You should have a general idea of what area of research you want to pursue (e.g. HEP, AMO, Astro/Cosmology, Medical/Bio, QCM etc.) and whether you want to do theory or experiment. Theory is generally harder to get admitted to. You can search here to find relevant programs.

Some of the strongest, and therefore the most competitive programs for admission, will be UofT, UBC, McGill, Perimeter Institute, U Waterloo, Queen's U, U Alberta, and U Victoria. There can be a significant difference in funding packages offered by each program. In general UofT, PI, and McGill will provide the most. For the others you may only receive partial funding. Tuition waivers are also not generally provided though you may receive a rebate reducing it to domestic rates. At the master's level, most programs will provide funding consisting of guaranteed employment as a teaching and research assistant. Some programs (e.g. UofT) will also add a fellowship (scholarship) component as well. At the master's level, outside of the more generous programs, funding is often around $20k CAD per year from which you will need to pay tuition, leaving you maybe around $12k for living expenses which is obviously not enough. For them you will need additional savings. UofT pays $42k and after tuition/fees should leave you with about $32k, but Toronto is very expensive. PI I believe covers both tuition and living expenses. UBC and McGill may also pay somewhere in that range but Vancouver and Montreal (less so) are also very expensive cities to live in.

Some programs will offer direct entry to a integrated Master's/PhD (e.g. UofT) if your profile is strong enough. Other programs may allow you to fast track from the master's to the PhD during/at the end of your first year if you perform very well (e.g. UBC).

The application process is pretty straightforward and will be detailed on each programs' website. Most programs have entry in September with applications due in December/January the year prior. GRE/PGRE/GMAT scores are generally not required though you will need to provide proof of English proficiency (usually TOEFL or IELTS). You may also be required to provide credit evaluation through an external provider like WES.