You should rarely add another answer if you already have one answer to that question.
To emphasise that it should be exceptional, when you click the link to add another answer, you get a friendly confirmation dialog:
But sometimes there are good reasons to post more than one answer to a question, therefore the functionality exists.
You should not split one answer into multiple posts, even if it is a long answer consisting of several parts. If the parts together make up the answer, it should be one post. (But, if you write the awesomest answer ever and hit the post-length limit, go ahead and break the rule.)
If you can offer substantially different answers to the problem, that can be a case where multiple separate answers are appropriate, but each should be able to stand by its own merits, of course.
Variations of the same theme belong in the same post, making more than one answer of them just adds noise.
Even if you suggest two unrelated ways to solve a problem, if they are short enough, they should usually be (separate) parts of one post, since more posts clutter the page. Unless they don't fit together. For example if one of them uses very controversial techniques, having them in the same post would make voting difficult. It would force people to a) upvote content they disapprove of, b) not upvote content they strongly approve of, c) downvote content they approve of, d) not downvote content they strongly disapprove of. Seems undesirable.
If putting both ways into the same answer would create an unreasonably long post, and the two ways aren't related, you should post them as separate answers. Two normal-sized posts are easier to digest than one humongous.
You should post multiple answers if they are unrelated and
- they are too long to be in the same post or
- they are superficially similar, so having them in the same answer could be confusing or
- they are so dissimilar that having them in the same answer would be incongruent or
- one of them is likely to meet objection and the other approval or
- you really think it would be better to have them in different posts.