Create a folder on your computer to contain music for your video. Call it "video music" to keep it simple. Fill the folder with MP3 music files you want to edit into your video project. Putting all the music files in one place makes it easier for you to import them en masse later.
Open your video editing program of choice and click "Import Media" under the editing program's "File" tab. Usually this is a universal trait of all editing programs--if your editing program doesn't have these tabs then consult the owner's manual.
Select the video you want to edit. When you do, it should import into the video editing program's "collection" folder, where all the media you're using in the project is stored--each media file is shown in a window in the editing program. Drag and drop your video onto the "timeline" at the bottom of the given video editor. The "timeline" is another universal feature of video editors, and will help you sync up music with the video.
Click "Import Media" under the "File" tab again, only this time browse and select the music you want to import. Once it's imported and in the "collection" folder, drag it to the timeline over the video. The music should sync to the video, but you can still slide it forward or backward with the mouse so that it matches up.
Trim the music track so that it matches up with the video. This is done by scrolling over to either side of the track--the music track is right below the video track. Now move the music track to the left or right to extend it or trim it to correspond with the video clip. Music edits can be very precise. Play around with various cues and ways to copy and add sections of the song to the video.
Copy and paste the trimmed music track to cut it into multiple files. For example, if you want the chorus to be used multiple times throughout your video, trim out everything else, then copy the selected track. Now paste it into your "collection" folder and you can place it in multiple areas in your video.
Export the project when finished as a video file using the editor's specific method for doing so--usually it is done by clicking "Save As, Movie File". But every editor is different so consult the manual. The video is now accompanied by the soundtrack music.