Look at the line across the top of your screen, whatever it's called. Mine has an American flag at the right side. Point the mouse to the flag: a pulldown menu should show the languages currently available. Choose on whichever language you want. I believe mine started with just American English and Chinese, but adding others is easy. At the bottom of the pulldown menu, click on "Open International". (You can also get here through System Preferences/ Personal: International/ Input Menu.)
On my laptop, I can select different ways of typing in a HUGE number of languages. There are five different input methods for Korean; the fourth one, Gongjin Cheong Romaja, works phonetically: if I type "m", I get the Korean character ㅁ (the square that indicates that sound in Korean). In the other systems "m" gets me - or ㅎ (first one the "yi" sound; second one the "h" or sometimes silent final sound, if I remember my Korean phonetics right). One of those five input methods probably matches the one you've memorized. Just select them all, toggle through, and see which one works.
(On choosing which input method: these may take some playing around with. I sometimes type in Chinese, and the "default" phonetic system was horribly nonintuitive and I had to de-select and select various options through submenus.)
Just check off the languages you want added to your input options. Then, when typing, you can click the flag in the top right corner of, uh, whatever that line across the top of the screen is called. Choose the one you want.
To toggle between the current typing language and the previous one, press Command + Space.
Note that my notebook shipped in Asia; perhaps North American ones don't have all the languages available.
Good luck!
