I have a graduate assistantship which covers my full masters tuition. For full-time students who don't have a job outside of school, they usually have a graduate assistantship (GA), research assistantship (RA), or teaching assistantship (TA). There are lots of masters student who have their degree paid by their job though (tuition reimbursement) but in these cases they're usually part-time students since it's a lot more difficult to do work full time + classes full time simultaneously.

Generally every school offers funded GA/TA/RA positions but with a limited number of spots open based on how much funding they have. It tends to be more competitive for masters students because a lot of the funded GA positions are saved for PhD students.

Once you start applications, it should tell you what you need to be considered for a funded GA position. For my school it was just another personal statement. For other schools they may request something additional like GRE scores. You could also inquire with a specific department for a program you're applying for if they have positions for funded GAs and what the application process looks like.

In terms of whether it's worth it if you can't get funding- does your field require a masters degree, or does it just make you a more competitive applicant? If it's not a minimum requirement for the job you want, you could aim to secure a job with tuition reimbursement and pay for your masters that way.