Okay... some music theater basics:

Musical theater is a broad term for theatrical performances that feature music as a central component and combines songs, spoken dialogue, acting and dance. While some musical theater composers create shows that incorporate other influences and musical traditions, Broadway composers tend to share a common musical influence of American musical theater.

so... a music theater composer does what?

At a high-level, a musical theater composer is responsible for a show's music. Most musical theater composers work with a development team that includes a book writer and lyricist who are responsible for the show's story, writing the script, and adding the lyrics. There are some versatile composers like Lin-Manuel Miranda, who take the creative process a step further by overseeing every aspect of a musical from start to finish.

In the "production stage" of a new show the composer will some times work with the music director to tweak the final performance based on the talent and physical setting for the show, but the music director is usually permitted to make minor adjustments to the score based the configuration of the ensemble, a singer's range and/or issues associated with staging, blocking and/or choreography.

and... "method composing", what the heck is that?

“Method Composingis a phrase sometimes used to describe the music composition process for music theatre works developed by April Alsup. Similar to "Method Acting", a well-known term used to describe the training and rehearsal techniques prominent at the Actors’ Studio in New York City and associated with actors such as Marlon Brando, Dustin Hoffman and Robert De Niro, "Method Composing" uses the same fundamental elements for creating the score of a musical theatre work. For example, in April's latest work "Eigg the Musical"  she used the accordion for the primary instrumentation since the show takes place during a typical ceilidh music festival and an accordion is often used for musical accompaniment or as part of a ceilidh ensemble in Scotland. April had never composed music for an accordion or a ceilidh ensemble, but nevertheless was up for the challenge and several years later performed the work on the accordion as part of the musical's ensemble at the 2023 Edinburgh fringe festival. Over the years the phrase "Method Composing" has been attributed to her music development process.

then, there's... "composer-led",  is that a music theatre development term?

Yes, when a composer decides much of the elements of the text, staging and design it is considered to be "composer-led". This is often a result of the composer formulating the basic  milestones for story and identifying unique musical characteristic for each character before identifying the book writer and the other members of the creative team. Examples of key music theatre artists who compose and direct their works include Georges Aperghis, Heiner Goebbels and of course, April Alsup. She, like other notable composers; Laurie Anderson, Meredith Monk and Robert Ashley, often perform their own works too. 

finally... is there a "right" or "wrong" way to write a new music theater work?

No! When it comes to writing music theater works, there really is no preferred method. Some musical theater composers just sketch out songs with chords, rhythm and a melody, leaving the instrumentation to an orchestrator. Others might deliver a fully orchestrated score with a specific ensemble and voices. Musical theater composers create music for all sorts of purposes, instrumental compositions might be used for underscoring or to enhance scene changes, highlight an onstage event, or support a dance number. Vocal songs often advance the plot, supplement story threads, or show a characters' emotions, struggles, and thoughts. There are so many examples of successful musical theater development teams and the process is different from team to team. The important thing to remember is that "there is far more we can do together than we can ever do on our own". Find the formula that works best for you and to enjoy the process.