Q:

Using Custom Data Types in Java

I am new to programming and I have an assignment to write a class called Names.   In my main method, I want to read in the entire name and pass it to my Names constructor.   However, I keep getting type mismatch errors when passing the method data.   What am I doing wrong?? 
import java.util. Scanner;
public class Names {
String first, middle, last;
    /**
     * @param args
     */
    public Names(){

    }
    public Names(String first, String middle, String last){
        first = this.first;
        middle = this.middle;
        last = this.last;
    }

    //returns the first name
    public String getFirst(){
        return first;
    }

    //returns the middle name
    public String getMiddle(){
        return middle;
    }
    //returns the last name
    public String getLast(){
        return last;
    }
    // Returns a string containing the person's full name in order,
    public String firstMiddleLast(){
        String ret = first + " " + middle + " " + last;
        return ret;
    }
    public String lastFirstMiddle(){
        String ret = last + ", " + first + " " + middle;
        return ret;
    }
    public boolean equals(Names otherName){
        if (first.equalsIgnoreCase(otherName.first) || middle.equalsIgnoreCase(otherName.middle) 
                || last.equalsIgnoreCase(otherName.last))
            return true;
        else
            return false;
    }
    public String initials(){
        String retVal = first.substring(0) + "."  + middle.substring(0) + "."  + last.substring(0) + "."; 
        return retVal.toUpperCase();
    }
    public int length(){
        String wholeName = (first+middle+last);
        int retVal = wholeName.length();
        return retVal;
    }
    public static void main(String[] args) {
        Names person1 = new Names();
        Names person2 = new Names();
        Scanner scan = new Scanner(System.in);

        System.out.println("Enter First Name: ");
        person1.first = scan.next();

    }

}

A:

For one thing your constructor is backwards.  Do this:
public Names(String first, String middle, String last){
    this.first = first;
    this.middle = middle;
    this.last = last;
}

The this reserved word always refers to the class/object you're working with.  So when you refer to this.first in the Names class you are referring to Names' first variable, not the function parameter you've also named first. 

A:

Line #60 when I try to pass the String first to the constructor
  Names(String first, String middle, String last)

I dont see any compile time error's in your posted code but your code should be like this:
    System.out.println("Enter First Name: ");
    String firstname = scan.next();
     System.out.println("Enter Middle Name: ");
    String middlename = scan.next();
    System.out.println("Enter Last Name: ");
    String lastname = scan.next();

    Names person1 =new Names(firstname, middlename, lastname);

And as noted by others your constructor declaration is not valid.  
 public Names(String first, String middle, String last){
        this.first = first;
        this.middle = middle;
        this.last = last;
    }

