What's the proper way to compare a String to an enum value?

I'm gathering from your question that userPick is a String value. You can compare it like this:

if (userPick.equalsIgnoreCase(computerPick.name())) . . .

As an aside, if you are guaranteed that computer is always one of the values 1, 2, or 3 (and nothing else), you can convert it to a Gesture enum with:

Gesture computerPick = Gesture.values()[computer - 1];

You should declare toString() and valueOf() method in enum.

 import java.io.Serializable;

public enum Gesture implements Serializable {
    ROCK,PAPER,SCISSORS;

    public String toString(){
        switch(this){
        case ROCK :
            return "Rock";
        case PAPER :
            return "Paper";
        case SCISSORS :
            return "Scissors";
        }
        return null;
    }

    public static Gesture valueOf(Class<Gesture> enumType, String value){
        if(value.equalsIgnoreCase(ROCK.toString()))
            return Gesture.ROCK;
        else if(value.equalsIgnoreCase(PAPER.toString()))
            return Gesture.PAPER;
        else if(value.equalsIgnoreCase(SCISSORS.toString()))
            return Gesture.SCISSORS;
        else
            return null;
    }
}

My idea:

public enum SomeKindOfEnum{
    ENUM_NAME("initialValue");

    private String value;

    SomeKindOfEnum(String value){
        this.value = value;
    }

    public boolean equalValue(String passedValue){
        return this.value.equals(passedValue);
    }
}

And if u want to check Value u write:

SomeKindOfEnum.ENUM_NAME.equalValue("initialValue")

Kinda looks nice for me :). Maybe somebody will find it useful.