You will need a "special" font to visualise the text but depending on the writing system it may be enough for someone to simply make one new glyph for each of the characters in your system and add it to a general purpose "everything" font. For some writing systems you need more powerful technology because e.g. the system has complicated rules about how shapes fit together and are transformed by adjacent shapes.
For practical purposes there isn't "something else". We're well past the point where Unicode was adding things that worked fine on a specially modified edition of Microsoft Windows for the specific language (like Dungan, which needs extra characters not normally used in Cyrillic) or whatever, these are now often _really obscure_ writing systems where previously you'd only put them "on a computer" by uploading a picture of the writing. Now the computer can handle them as text because they're in Unicode.
For all the historical writing systems, and some of the minority systems that have very few users many of whom know another language that is more widely used and thus more useful to them in practice (imagine going on a forum to ask a question about maintaining the motor sledge you use, you know Russian and also Dungan - obviously you will ask in Russian, because that's a LOT more people who might answer) - in practice the new scripts in Unicode will only be used by academics to transcribe stuff. It still makes that easier, because they can use Unicode everywhere, not just in specialist tools that maybe another researcher built for the language they care about.