Ultra-basic idea...
Pick a year, then
do some math to find
a day-of-the-week.

That's our "Doomsday".

Each month of that
year has a date we
can reference as the
same day-of-the-week
as that "Doomsday".
The base "century part" of 2015 is 2000
The "year part" of 2015 is 15

The base-doomsday for century 2000 is 2 (from Table X)

Now, complete this sum:
baseDoomsday+year+round( year ÷ 4 )=
2+15+round( 15 ÷ 4 )=
2+15+round( 3.75 )=
2+15+3= 20

Now divide that total by 7 and get the remainder...
total÷7 =        
20÷7 = 2 with remainder 6
This remainder, 6, is the Doomsday for 2015. Day 6 is Saturday (from Table Y).

So now we must see what date, in our month (Jul 2015), is a "Doomsday Saturday".
The doomsdate in month 7 (Jul) is 7/11 (from Table Z).
And now we know that 7/11/2015 was a Saturday!

And 7/4/2015 was also a Saturday
So...
7/3/2015 was a Friday

TABLE X
base
centuries
base
doomsday
1500190023003
1600200024002
1700210025000
1800220026005
* You probably only need to
remember the red years!
TABLE Y
week dayday num
Sun0
Mon1
Tue2
Wed3
Thu4
Fri5
Sat6
TABLE Z
MonthDoomsdate
JanJan 31st (or Jan "32nd" in leap years)
FebFeb 28th (or Feb 29th in leap years)
MarMar "0th"
Other odd#
months
4/4, 6/6, 8/8,
10/10, and 12/12
Other even#
months
5/9, 7/11, 9/5, and 11/7
(Remember: "I work 9-to-5 at the 7-11")