When I use the console it says Syntax Error. I then tried to check if I have the group ownership; I'm shown as a normal user and this permissions.yml file changed nothing: no color, no prefix as Owner or anything!

Would any of you help me figure out what I did wrong?

groups:
    default: 
        default: true
        prefix: '&2Default&2'
        permissions:
        - modifyworld.'
        - -essentials.item
        - essentials.sethome
        - essentials.home
     Co-Owner:
        default: false
        prefix: '&5Co-Owner&5'
         permissions:
         - *

Users: 
    crazy_man_12
        group: Owner
        prefix '&4'        
        permissions:
        - *

Users:
    captain_colors50       
        group: Admin
        prefix: '&0'
        permissions: 
        - *        

I assume that you are running a CraftBukkit server. Each permission system for CraftBukkit is different, and has a slightly different way of structuring their config files, thus it is very difficult to give plugin-specific help for your problem. That being said, at first glance there are a multitude of potential problems in the given file:

Problem #1 is 'modifyworld.' '. I have never seen nor heard of a permission that ends in '.' ', perhaps you meant to use 'modifyworld.*'?

Problem #2 is not really a problem. You have your prefix variable for default as '&2Default&2'. The second '&2' on the end is not necessary to change the color of the text, only the code before the prefix text. Additionally you could add '&r' to reset the color before the actual player name is printed. This problem also occurs in '&5Co-Owner&5'.

Problem #3 is in the naming if the Co-Owner group. The '-' in the name could possibly be disrupting your syntax, thus throwing the 'Syntax Error' on your console.

Problem #4 is that you have two 'Users' tags. Instead of:

Users: 
    crazy_man_12
        group: Owner
        prefix '&4'        
        permissions:
        - *
Users:
    captain_colors50       
        group: Admin
        prefix: '&0'
        permissions: 
        - *        

You could use something more like this:

Users: 
    crazy_man_12
        group: Owner
        prefix '&4'        
        permissions:
        - *
    captain_colors50       
        group: Admin
        prefix: '&0'
        permissions: 
        - *        

Problems #5 and #6 are also in this section. You need a colon after each of the player names for correct YAML structure. Also, you may need to use 'users' instead of 'Users' (lowercase vs. uppercase).

Lastly, Problem #7 is that you have your two listed players in non-existent groups. You need to assign them to existing groups for their permissions to work.

In conclusion, your fixed file could look something like this:

groups:
    default: 
        default: true
        prefix: '&2Default&r'
        permissions:
        - modifyworld.*
        - -essentials.item
        - essentials.sethome
        - essentials.home
    CoOwner:
        default: false
        prefix: '&5Co-Owner&r'
        permissions:
        - *
users: 
    crazy_man_12:
        group: CoOwner
        prefix '&4'        
        permissions:
        - *
    captain_colors50:    
        group: CoOwner
        prefix: '&0'
        permissions: 
        - *