I'm not sure how representative it is of the "right" way, or even a common way, but here's the rough workflow my puzzles go through (sorry in advance for the wordiness).
1. Play to your strengths
You say you don't have any programming knowledge, great! Now you know where not to start. Have a dig through the tags and see what jumps out at you. Browse some existing content and see what you gravitate towards. If you like the sound of something, but don't have any experience, go through the top puzzles in that tag and either read through the accepted answers, or better yet, have a crack yourself - you'd be surprised how quickly you can pick up seemingly impenetrable topics.
(Also as an aside, the riddle sandbox is probably actually a great opportunity for you, as you'll get feedback on your ideas so you can iterate/polish rapidly with more experienced puzzler's help).
2. Brainstorm
Keep a notebook (or text file, or note keeping app, etc) and just dump anything in that pops into your head. It doesn't have to be complete ideas, it can just be fragments, or themes, or story ideas, etc. A lot of what you capture will be discarded or go nowhere, but you'll also find that random fragments tend to naturally clump together.
- Observed that dice can be called "bones" in slang and that the singular is "die"?
- Just learned what an ambigram is, or what amphibrach meter is, or a heteronym?
- Standing in the shower wondering if you could make a fractal sudoku?
- Noticed the little shapes in the background of the PSE site and wondered how you could build a puzzle around them?
- Realised that all matter is merely energy condensed into a slow vibration?
...Awesome, write it all down.
Note: At any point from here on, you need to be willing to throw things away and go back a step or more (see refine for more). Don't force an idea - all ideas are made better by what's left on the cutting room floor, and sometimes a discarded idea can get resurrected months down the track when you have a new insight.
3. Iterate
Ok, I've got the best idea ever, I'm going to click that "Ask Question" button over there and start writing it up.
Not so fast, you've barely started... Once you've got some random fragments of ideas, pick one or two and start to flesh them out. Obviously this step is very vague, and the exact process will depend heavily on the type of puzzle you're creating, but generally try to ask yourself questions like:
- What does the goal/solution look like?
- How can I get there? (often working backwards from a goal makes puzzle creation easier)
- Is my solution unique and well defined (and will you know it when you find it)?
- How am I going to present this (theme, story, visuals, etc)?
- How will solvers try to solve this?
- How can I distract solvers from the true path?
- How can I guide solvers towards the true path?
- What ties these ideas together?
- What other related ideas can I bring in to add interest?
- What extraneous ideas can I cut to hone and bring cohesion?
- If I didn't know the answer, could I solve this?
During this phase, anything goes and your puzzle will likely be changing a lot as it evolves. Don't be afraid to try random ideas out or try to mash multiple layers/ideas together. Don't be afraid to discard ideas, even if you've put work into it - remember the idea still exists, and may resurface later, plus you learned a bunch while trying things out.
Also, don't be afraid to "borrow" ideas from other puzzles, especially while you're learning, it's a great way to get started, and if you continue to iterate and refine, the borrowed idea will likely dissolve away and just become "inspiration" anyway (just be sure, when you get to later steps that you haven't outright plagiarised anything).
Note 2: All steps presented here, but this one in particular, don't represent work performed in a single "session", it is often five minutes musing here, thirty minutes trying out an idea there, a midnight waking with a new idea, a scrawled brain dump in a notepad, etc, that continues to evolve over a period of time. You'll also often find yourself with multiple "active" ideas running in parallel as you go.
4. Refine
Awesome, I've got a working puzzle, can I post it now?
Nope sorry, once you have something resembling a complete puzzle, it's time to refine things. This stage is all about trimming out extraneous ideas and tidying things up.
This is the step that people often skip, much to the puzzle's detriment. It can also be the hardest... that awesome idea about doing it all in French, or that stanza you shoehorned in because you liked the rhyme it produced? Does it still work, is it bringing anything to the table? You need to be willing to let go of ideas if they don't actually add something to your puzzle (don't forget, they can always come back another time in another puzzle).
If it's a riddle, spend some time smoothing out the meter/rhyme. If it's a visual puzzle, tidy up your images and make sure things are consistent and look good. If it's a pattern, make sure you're providing enough data points. Flesh out the story/presentation.
Go through the questions listed in the Iterate section and make sure you can answer them, but during this stage, the most important one is to MAKE SURE YOUR PUZZLE HAS A PATH TO SUCCESS! By this, I don't mean that a good puzzle must be solvable (although that's obviously important :P), what I mean is that a good puzzle doesn't present an insurmountable wall, it presents a challenging path.
Ideally, you want to pepper hints into your presentation (in wording, in visual style, etc) that help to nudge solvers in the right direction. If it's a multi-stage puzzle, the solution to one stage should provide new information that acts as a hint to the next. Just be careful not to provide too much direction (and feel free to throw in some misdirection), because you still want it to be a challenge. Think about what leaps of logic are required at any given point - if you have to make to big a leap, or worse, multiple leaps at once with no way of verifying the intermediate steps, it's likely going to be too hard (and not fun). All that being said, balance is difficult, and you will get it wrong, especially initially, just learn from those experiences and you'll improve.
5. Polish
Jeez Alconja, I'm getting bored of my own idea, can I just post the damn thing?!
Sorry, no, still one more step. At this stage your puzzle is good, it's solvable, it's refined, but I guarantee you've made a mistake. Go over it one last time with a fine-toothed comb (or get someone else to take a look) and make sure there's no spelling/grammar issues, make sure your images are clear, that stack exchange doesn't mess with your layout/formatting, etc.
...Ok, now you're good to go.
Final note: It may seem as if the above is written with the assumption that you'll be trying to make a massively elaborate, multi-layered, puzzle, but I think it still applies to the simplest of riddles. Don't be daunted or put off by my wall of text, it may look complex and/or time-consuming, but it doesn't have to be. I guess if I can give you one piece of advice, it's simply to try and not rush a new idea out. Let it stew for a bit, write it, hone it, let it sit some more, re-read it, etc, and you'll end up with a much better puzzle than you started with.
