Once you have an idea of what you want to do you have to choose the program most convenient for your needs.
If you are a beginner, there is nothing like Windows Movie Maker. This simple program included in Windows is quite easy to use. First you import your video, allowing the program to cut it into short chunks that are aligned in chronological order for you to reorder in a second window that has a timeline.
The timeline is the video you are creating and will have two tracks that run at the same time: the video and the music.
Windows Movie maker has even very simple but effective and professional effects to make transitions between scenes, you can superpose scenes and they will fade into one another, change colors, go slower or faster, etc
As you work with your video, you can keep on previsualizing it in a third window, that will allow you to see how it play in real time.
Finally, once done, you should save the video, rendering it either into format wmn or avi depending on your needs (wmn will be less heavy). Both formats are acceptable in sites such as Youtube.
Once you have managed to command well Windows Movie Maker you can upgrade yourself, depending on your needs to other edition software packages that allow even better liberty. These programs work in a similar fashion than WMM, they use timelines and multiple tracks of video and music, have possibility of managing a wide variety of special effects and a very delicate manipulation of quality and color.
For instance, there is Adobe Premiere, a video editing software that is part of the Adobe Suite (together with programs such as Photoshop, Illustrator, Dreamweaver, etc.)
Another possibility is Sony Vegas, a widely used program preferred by many professional and semi profesional video editors and that is free for trial (you can google it and download it). I will warn you that it is a little complicated to learn, but you can get some very nifty tutorials for free on Youtube that will save you a lot of inconvenience.
For expert users (who probably won’t need this article anyway), there is the famous Finalcut for Mac. In addition, another new core professional editing tool is Avid. It is quite expensive and requires a very powerful machine but learning this program may even land you a job as professional editor, so if you can afford it and interest you for real, go for it.