Partially answered in comments:
The right method (a) matches your ideas of what you are estimating and (b) works well with your data to the extent allowed. (Not all samples have well-defined modes; no white magic will extract a worthwhile estimate in those cases.) That may seem a worthless answer, but you haven't given enough information to allow guidance. Why do different methods exist, any way? You might try various methods, see if they agree, relating results to various different graphs of your data and your scientific understanding. In this context, there is no such thing as "just plot[ting] the distribution"! – Nick Cox
The mode is sometimes well-defined for discrete data. Otherwise there are numerous different ways to get at it. Even if you focus on kernel density estimation (which is only one method among several), there is always a choice of kernel type and width before you can get the position of the maximum density. So, I'd this follows from any survey of density estimation alone, without needing a wider context. Modes tend not to be discussed seriously in introductory texts or courses. – Nick Cox
Since mode is not always welldefined/uniquely defined, mode is often a not very helpful concept. That is probably a reason why it is little discussed in texts, little formal statistical analysis is based on modes.