There is the single character viewpoint. Though this can be done in third person, usually a writer chooses first person. This helps the reader really get into a characters head. Usually done in past tense. Sometimes writers use the present tense. Nothing wrong with that. I don't enjoy this kind of telling since most of the time I can't get into the character since they're so not me.
There are a number of ways to use multiple character viewpoints. One often used in romances is the hero, heroine way with each getting time on stage. Sometimes here a third person leaps in' Usually this is the villain and can add a depth to the story.
Then there is the use of multiple viewpoints and here there can be problems. The reader can become confused when the viewpoint character shifts too frequently in the middle of a scene. I've even seen it done in the middle of a paragraph and once in the middle of a sentence. This can also become more of an outside force or the author telling the story.
But these are the general ways. Later we'll look at them to help you find what works best for you.