I've written this program using Java in Eclipse.
I was able to utilize a formula I found that I explained in the commented out section.
Using the for loop I can iterate through each month of the year, which I feel good about in that code, it seems clean and smooth to me. Maybe I could give the variables full names to make everything more readable but I'm just using the formula in its basic essence :)

Well my problem is it doesn't calculate correctly for years like 2008... Leap Years.
I know that if (year % 400 == 0 || (year % 4 == 0 && year % 100 != 0)) then we have a leap year.

Maybe if the year is a leap year I need to subtract a certain amount of days from a certain month.

Any solutions, or some direction would be great thanks :)

package exercises;

public class E28 {
/*
 * Display the first days of each month
 * Enter the year
 * Enter first day of the year
 * 
 * h = (q + (26 * (m + 1)) / 10 + k + k/4 + j/4 + 5j) % 7
 * 
 * h is the day of the week (0: Saturday, 1: Sunday ......)
 * q is the day of the month
 * m is the month (3: March 4: April.... January and Feburary are 13 and 14)
 * j is the century (year / 100)
 * k is the year of the century (year %100)
 * 
 */
public static void main(String[] args) {
    java.util.Scanner input = new java.util.Scanner(System.in);
    System.out.print("Enter the year: ");
    int year = input.nextInt();

    int j = year / 100; // Find century for formula
    int k = year % 100; // Find year of century for formula

    // Loop iterates 12 times. Guess why.
    for (int i = 1, m = i; i <= 12; i++) { // Make m = i. So loop processes formula once for each month
        if (m == 1 || m == 2)              
            m += 12;                       // Formula requires that Jan and Feb are represented as 13 and 14
        else
            m = i;                         // if not jan or feb, then set m to i

        int h = (1 + (26 * (m + 1)) / 10 + k + k/4 + j/4 + 5 * j) % 7; // Formula created by a really smart man somewhere
        // I let the control variable i steer the direction of the formual's m value

        String day;
        if (h == 0)
            day = "Saturday";
        else if (h == 1)
            day = "Sunday";
        else if (h == 2)
            day = "Monday";
        else if (h == 3)
            day = "Tuesday";
        else if (h == 4)
            day = "Wednesday";
        else if (h == 5)
            day = "Thursday";
        else 
            day = "Friday";

        switch (m) {
        case 13: 
            System.out.println("January 1, " + year + " is " + day);
            break;
        case 14:
            System.out.println("Feburary 1, " + year + " is " + day);
            break;
        case 3:
            System.out.println("March 1, " + year + " is " + day);
            break;
        case 4:
            System.out.println("April 1, " + year + " is " + day);
            break;
        case 5:
            System.out.println("May 1, " + year + " is " + day);
            break;
        case 6:
            System.out.println("June 1, " + year + " is " + day);
            break;
        case 7:
            System.out.println("July 1, " + year + " is " + day);
            break;
        case 8:
            System.out.println("August 1, " + year + " is " + day);
            break;
        case 9:
            System.out.println("September 1, " + year + " is " + day);
            break;
        case 10:
            System.out.println("October 1, " + year + " is " + day);
            break;
        case 11:
            System.out.println("November 1, " + year + " is " + day);
            break;
        case 12:
            System.out.println("December 1, " + year + " is " + day);
            break;
        }
    }
}
}