Here are some shortcuts / tips to find out the day of the week from the given date...

Day of the Week: January has 31 days. It means that every date in February will be 3 days later than the same date in January (28 is 4 weeks exactly). The below table is calculated in such a way. Remember this table which will help you to calculate.

January   0
February  3
March     3
April     6
May       1
June      4
July      6
August    2
September 5
October   0
November  3
December  5

Step 1: Ask for the Date. Ex: 23rd June 1986.
Step 2: Number of the month on the list, June is 4.
Step 3: Take the date of the month, that is 23.
Step 4: Take the last 2 digits of the year, that is 86.
Step 5: Find out the number of leap years. Divide the last 2 digits of the year by 4, 86 divide by 4 is 21.
Step 6: Now add all the four numbers: 4, 23, 86, 21 which sums to 134.
Step 7: Divide 134 by 7 = 19 remainder 1.

The reminder tells you the day.

Sunday    0
Monday    1
Tuesday   2
Wednesday 3
Thursday  4
Friday    5
Saturday  6