C# Public Enums in Classes

Currently, your enum is nested inside of your Card class. All you have to do is move the definition of the enum out of the class:

// A better name which follows conventions instead of card_suits is
public enum CardSuit
{
    Clubs,
    Hearts,
    Spades,
    Diamonds
}

public class Card
{
}

To Specify:

The name change from card_suits to CardSuit was suggested because Microsoft guidelines suggest Pascal Case for Enumerations and the singular form is more descriptive in this case (as a plural would suggest that you're storing multiple enumeration values by ORing them together).

You need to define the enum outside of the class.

public enum card_suits
{
    Clubs,
    Hearts,
    Spades,
    Diamonds
}

public class Card
{
     // ...

That being said, you may also want to consider using the standard naming guidelines for Enums, which would be CardSuit instead of card_suits, since Pascal Casing is suggested, and the enum is not marked with the FlagsAttribute, suggesting multiple values are appropriate in a single variable.

Just declare the enum outside the bounds of the class. Like this:

public enum card_suits
{
    Clubs,
    Hearts,
    Spades,
    Diamonds
}

public class Card
{
    ...
}

Remember that an enum is a type. You might also consider putting the enum in its own file if it's going to be used by other classes. (You're programming a card game and the suit is a very important attribute of the card that, in well-structured code, will need to be accessible by a number of classes.)