What is the difference between different words of "note" - 便条，笔记，备忘录?
便条 (note; scrip)  mostly refers to a 'short informal handwritten note' that is written in very short time to deliver a simple message- usually contains no more than a sentence or two, sometimes even just one word. 

A note on the table that said: "Back at ten, dinner in the fridge. - Mom" is a typical 便条. A stranger handed you a piece of paper that said "RUN!" is also a 便条

笔记 (note; notes) as a noun can be short for '笔记本'(notebook). The most typical one is school notebooks where students write down summaries of lectures, main points of a lesson or any useful information that can help them study later.

Notes written on loose paper can also be called 笔记. For example, copy of written text on blackboard, notes took from a speech are all 笔记 

The act of taking notes is 做笔记

备忘录 (memorandum; memo) mostly refers to a document that serves as a  'reminder'.  It can be personal or official; hand written or printed; in single sheet of paper or a whole book long.


  How can I use them properly? For example, if I create an article that takes note of programming tips in order to refer to sometimes in the future, which word fits the best?


That would be your 'personal notebook' (个人笔记)