This is a great start:www.ticalc.org/programming/columns/83plus-bas/cherny/
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and check out this guy's instructables:https://www.instructables.com/id/Ti_84_amp_Ti_83_Programming_Lesson_3/
The calculator either came with a thick book (like mine did) or a cd. If not - check the TI website. They have documentation on the entire language.
The easiest way is with TI-BASIC, the program language that treats every line of code as if you're typing it in on the main screen - from input to output.
Start by making a program, call it HELLO
in the program, put the code (you have to pull each command out of the menus in the ti-83)
Disp "HELLO WORLD"
exit (which will save what you've put, then execute the program
What does it do?
CLS clears the screen
Disp outputs on the current line (like an old printer would), whatever you put in quotes.
There are too numerous functions to explain how to program here. Check out the tutorials on the texas instruments website (www.ti.com) and I think they have support at ti-calc.org
You will find useful: Disp, If, Then, Else, End, While, + - / *, and variables.