If you want to just replace the games music with your own, it is quite easy.
1. Convert your desired tunes into .ogg format (there are several free converters out their).
2. Find your mod folder. Create a new folder called "My Music Mod" or something.*
3. In that folder, create a folder called "Sound"
4. Paste your converted .ogg files into that sound folder.
5. Go to the Sins directory and find the sound folder there. Among the files you should see things "Advent 1" or "Battle 3" etc. These are music files (anything longer than 30 seconds probably is a music file). Rename the music in your mod to exactly the same name as these, and whenever that track would play, your new track will play instead. (Note for the main menu music, it is something like Opening Theme for Sins/Entrenchment and TEC 3 for diplomacy).
6. Start sins and go to the options in the main menu and hit the mods tab. Enable your music mod and your new music should will start appearing.
*If you don't know where this is, go to the mod tab mentioned in step 6 and hit the "Show Mod Path" button and it will display it for you. Note that one of the folders is a hidden folder if you have trouble finding it.
If you want to add music in addition to what is there, will that is a lot more complicated, so I won't get into that unless you really want to do it.