Inserting custom music
Mega Man Maker comes with the default music from the NES games plus some added by the developers, but you can insert your own music tracks. Please note that this is not a feature built into the game, so you'll have to do it outside of the game.
The file format that the game uses is .nsf (NES Sound Format) which is a format that a real NES and emulators can read and play. Mega Man Maker uses a player called the chiptune player that accurately emulates the sound of the NES. It also supports 3 of the 6 audio expansion chips. The Konami VRC6, Namco 163 (also called the Namco 106), and the Sunsoft 5B (also called the FME-7).
Choosing your Music
There are many ways to obtain .nsf files. The easiest way is to download .nsf files from online archives like Zophar's Domain and OCRemix. These sites contain .nsf files from NES games so you can download your favorite games' .nsf files. This isn't recommended though since Mega Man Maker only plays the first track in the .nsf file. You can also download .nsf files posted in the #nsf_replacements channel in the Mega Man Maker discord. The files posted there contain only 1 track, so it's perfect for playing in game. The (possibly) hardest way is to make your own using a program capable of making .nsf files. The recommended tool for this is 0CC-Famitracker. You will need to learn how to use it to make good music though.
Inserting the Music
To insert your .nsf files, go into your Mega Man Maker directory, then go into the Music folder. You'll be presented with a few folders. They're self-explanatory. Enter the folder to find the file from the game or category you want to replace. Rename your nsf file to the track you want replaced with. For example, if I want to replace Cut Man's theme with my own music, I would go into the "MM1" folder and rename my .nsf to "Cutman" and replace the regular .nsf with the custom one. Now your music will play when you select the track you replaced your nsf with.
Note that this is only client side, which means when uploading levels, only you will hear your music tracks. You'll also need to do this every time the game gets an update.