Hello! I am trying to program an arduino uno so that when I push a button it will ad 1 to a 4 digit seven segment display .
This is how it is wired.
Arduino pin -- Pin on 7 segment display
1--14
2--16
3--13
4--3
5--5
6--11
7--15
8--7
9--1 (resistor)
10--2 (resistor)
11--6 (resistor)
12--8 (resistor)
And My set up and parts is exactly the image below.

Yes
It looks like your switch is connected to +5V.
Try connecting it to GND.
Then use:
pinMode(YOURpinNUMBER,INPUT_PULLUP);
Need a link to the display
If it is a simple display, you should have 7 resistors, one for each segment, not 4 which sounds like one for each digit.
LarryD:
Need a link to the display
If it is a simple display, you should have 7 resistors, one for each segment, not 4 which sounds like one for each digit.
It's not a simple display, it's a 4 digit seven segment display (I'm assuming simple display is just one digit but I may be wrong).
And the way I have it wired, the bottom 8 pins of the display are what is numbered 1-8 and the top ones are numbered from 11-16. It should be wired correctly according to what I posted.
Also my button is in pin 13 and GND now.
The link you gave shows a common anode, four digit, simple 7 segment display.
A simple display is one that is only LEDs i.e. One with no driver.
Yours requires a series resistor, one for each segment.
7 segments.
Show us your sketch, attach it using the </> icon in the posting menu.
.