How can a master student get research opportunities?
Find the hallway where your department's faculty have their offices.

Knock on the first door.

When the professor answers, say "Hi, I'm [name].  I'm a master's student, and I'm interested in doing research.  Do you have some time to talk?"

Repeat for the remaining doors.

(It also helps to have some idea what kind of research you want to do, and to do some background reading on the professors' research before you talk to them.  We like it when students say "I read your paper on X, and I have a few questions.")