One of the main issues when hiring a composer to create songs for a project is communication. This and the fact that people can describe the same exact sound in various ways, sometimes even with contradictory descriptions doesn’t help the situation. Some people simply can't find the words, or afraid of using the wrong terminology. The following comes from my experience as a composer and aims to help with those issues.
The Essential
1. Provide the emotion/mood desired from each song
One of the most important step is to let the composer know what mood or emotion the song(s) is suppose to convey, or for what scene it will be used. This is pretty self explanatory.
2. Provide reference songs/Explain how they are to be used
Reference songs are huge. Find a song you like and present them as a guide to what you're looking for. Much like you would provide a artist with an example of the drawing style you would like them to produce. Just be sure you're clear on how the reference tracks are meant to be used. For example, it's probably best to find a song that's very close to what you're looking for, rather then supply many guide songs that are suppose to be meant for one single song.
However if that's not possible and you do go down that route, convey exactly what you like about each track and what elements you would like. Otherwise it can get very confusing for both parties and you'll end up with a song with parts you didn't even want.
Lastly be sure if your providing non gaming music as references, make clear that you want the tracks created to be played for the type of game you are creating, in this case VN's. Otherwise you may confuse the composer and although they might make a great sounding song, it may not fit your game.
3. Communicate in a plain/logical/constructive manner.
There's no need to use fancy music terminology, particularly when you're unsure of what it means. When communicating with a composer, usually the most simple and plain way to explain things is often the best. For example, the way you mentioned what was lacking from the sample you received is actually pretty good feedback .I.e " more emotion than was needed for a plain dramatic scene, but did not evoke as much emotion to be played during the climax." Depending on what direction you wanted to go in, either more emotional, or less, most composer would know what to address with that feedback to achieve it.
You don't need to over think things as much as it may seem. Say you want an instrument removed from a ceratin section of the song, but you don't know what that section of the song is called, simply providing the timestamp of where that section or instrument occurs is more than enough.
And this should be obvious, but make sure to provide constructive criticism, not blanket statements, like "this sucks, or " that part sounds like crap" which does nothing to help anyone. As hard it may seem to imagine, there are people with poor communication skills such as these. I've actually run across a few and had to leave and return what I had already been paid because progress came to halt, and achieving what couldn't be explained became nothing but a headache.
____________________
To surmise, be sure to take the time to decide on the direction of the music, find reference tracks and make a list of the songs needed and what emotion or mood they will be used for. If you can provide these things you're good to go. However, trying to compose without these things is incredibly frustrating, slow and a time wasting, guessing game.
The Helpful, but not Necessary
Here are some extra helpful things you can do to communicate song ideas with a composer, but are not as necessary
1. Provide useful project info
You can supply the following to the composer if available; the plot or setting of the game, a synopsis of the character personalities (especially useful for composing character songs) and any art, even if it's just a logo. I find all of these can help further guide and inspire the composition of a track.
2. Learn basic music terminology.
Music theory isn't really necessary to communicate, but knowing some basics couldn't hurt. For example, the difference between a note or chord, knowing some basic song structure ideas like verses, choruses, intros and bridges. And maybe knowing the difference between a melody and harmony. As well as knowing what tempo, beat and rhythm is. They can come in handy when you want to be more precise with your words and most composers will know these basics too.
3. Learn the names of common instruments/what they sound like.
It's the same thing when it comes to instruments. Although not necessary, it's good to know what some basic instruments sound like so when you get a composition back and hear something you like or don't like, it's easier to communicate with the composer on what that might be. This can make any changes to the song a great deal easier.
Sure, everyone knows what a piano sounds like. But say you have a drum beat and you don't like a certain sound the drumkit is giving off. Trying to communicate this to the composer, and then them figuring out what you mean can take quite a bit of trial and error. As opposed to you knowing that the particular sound you don't like is the snare of the drumkit, and thus the composer knows immediately and exactly what you mean. You can easily learn what some basic instruments sound like with the help of youtube and looking up instrumental songs or solo instrumental compositions. Wikipedia is also quite handy for research purposes.
____________________
As long as you follow the essential 3, you should be good with any composer. I've dealt with people who had little to no knowledge on music, but were still able to communicate and get the results they wanted.