3 Answers

List the reasons you feel he should be evicted, Get the majority of the tenants to sign it, send it to the complex management office. It doesn't really have to be all that formal. 

The trick is to have the other residents and the Community Manager agree... If they are paying their rent on time and haven't trashed their apt or exterior it will be hard for the Management to find cause for eviction.

On what basis or bases are you trying to pursue the eviction.  You need to check if the apartment complex has any by laws, covenants, or house rules that you can use to determine the possibility of eviction.  Unless he breaks these rules (on several occasions), it may be hard to kick this tenant out.  Also, if noise is a factor, then the police should be consulted.  The mere fact that you don't like his face or that he is person belonging to a minority group alone is not a good enough reason.    Document all violations and take pictures to back you up.   

If you live in co-op, it is generally possible to petition the owners in the building to evict someone.  Certain type of discrimination is permissible: building for the elderly only (young people may not live there).

Good luck.