In short, Paul is directing us to not act like the world. We are to act like Jesus instead through the guidance of the wisdom of His word. This specific passage removed from its context seems to direct the believer to completely remove himself from worldly culture and interaction with non-believers. In addition to the specific moral exhortations (i.e. do not lie), there is the direction to come together as one body of believers separate from the world.
It is important to understand, however, that this comes after verse two where Paul directs the reader to “set your mind on things above, not on the things that are on earth” (NASB).
The following passages also deal with where the mind of the Christian is to be, not where his body shall be. While his body can be out in the culture amongst sinners (just as Jesus’ body was during his earthly ministry), the mind of the believer is focused on heavenly things and the salvation of the sinner (just as Jesus’ mind was during His earthly ministry). This passage must be taken in this context and not be used to support monastic separation. In a fallen world, we can never be separate from the things that are fallen. Everything around us is not what it was meant to be. Complete separation is impossible. It is our responsibility, then, to be in the world (“put [it] aside”) without being like the world (“put on the new self who is being renewed”).
I personally attempt to accomplish this by trying to emulate Jesus in all that I do. I am not successful all of the time and sometimes it is very difficult to not be like the world, but it is my hope that I do a better job in each situation that I am in so that next time I am just a little bit better. I know that I can never be perfect like Christ and even if I get twice as good each time I’ll never reach the goal until final perfection comes. This can even be mathematically expressed: suppose you got rid of half your sin each day and your original sin level was 100. The next day it would be 50, the next 25, etc. If this number is divided in half forever it will never reach zero.