The process which makes this change is called Mastering. Begin by reading some articles on what mastering a song/album is. The tools used to make it look like that are compressors and limiters. These are just one part of the mastering process. To get it looking like professional 'masters' while not sounding extremely bad takes years and years of experience. It's not an easy task.
Keep in mind that compressing your music to look like this changes the sound. If you take it to extremes, it can degrade the sound quality. Subtle and well implemented compression can make it actually sound better, which again takes much skill. A large amount of music out there today is actually overly processed so the signal quality does in fact degrade. What they are trying to do is make that song as loud as possible when compared with another song whilst having the volume knob in the same place. Many believe this is kind of pointless (as do I). If the consumer wants it loud, they should just turn up the volume knob. But I digress.
In short, you have no hope of learning it over night. Don't expect to compete with professional stuff for a very long time yet. Experiment, see how it sounds using limiters, and then compare back to the un-processed version (at the same perceived volume). Once you can hear the quality degrade, stop and back off a little. For now, this is probably as far as you want to go. Be happy with what you have cause the next level up from this takes a little more time to learn! So get reading and get learning!