The instructions for entering, running, exiting, and editing are the same for any program. The actual program on this sheet allows you to quickly evaluate a function. This may be helpful when determining a reasonable window for graphing or investigating the value of a limit.  
Information that is printed within {} is not typed into the calculator. Usually this contains instructions for finding a particular command. Anything in RED denotes a button on the calculator. For example + is the addition button. Anything in BLUE denotes a button on the calculator that requires hitting another button first. For example the QUIT command will appear here as QUIT because you need to hit the 2nd button first.
Your calculator manual will be very valuable for finding the commands and buttons needed for programming. If you have misplaced yours, visit the TI website to view a copy. TI Manuals

If you have a TI Connectivity Cable, you can download the program EVAL.83p

How to enter a new program

Any words in the program that begin with an uppercase letter (Disp, for example) are actually commands and should be retrieved from a menu or key. In most cases the commands can be found using a menu at the bottom of the screen: PRGM, DRAW, VARS, or TEST. If you need to delete a character use DEL. It deletes to the right of the cursor. If you need to insert characters use INS. It inserts to the left of the cursor.

The Program
This program has four lines. Hit ENTER at the end of each line. When you are finished, hit QUIT.
:Lbl 1  {Lbl is in PRGM under CTL} 
:Prompt X       {Prompt is in PRGM under I/O} {X is the X,T button}
:Disp Y1  {Disp is in PRGM under I/O} {Y1 is in VARS under Y-VARS} 
:Goto 1  {Goto is in PRGM under CTL} 

How to run a program