Somewhere, towards the beginning of Game's Workshop's foray into Warhammer 40,000, or maybe from FASA's first edition of Battletech, there must have been a studio painter who really, really liked hazard stripes. As the hobby advanced, this pioneer's fetish became a standard for all around him, in ways that look rather interesting, but haven't got a whole lot to do with actual hazard safety.
I mean, do we really need to have stripes telling us that chainswords are dangerous? We don't mark out actual chainsaws that way, and for the most part those ones aren't designed with combat in mind.
Anyway, this mainstay of the hobby has endured in some form or another for the past thirty years or so, and is now a sort of 'classic' look that many painters like to employ.
My method for applying hazard stripes is fairly simple. The first thing I usually do is paint the area white.
The most obvious use of the white coat is to help the yellow show up, because no matter what brand of paint you're using, yellows are some of the hardest to get a good coat of paint on the mini with.
The other thing this allows me to do is shade and highlight the whole area with the white. This shading/highlighting helps to make the area pop and not look flat next to the rest of the mini.
I normally add the stripes onto the white before applying the yellow. The real trick to doing the stripes is to not worry too much about getting them straight the first time. Try and make them more or less even, and when you mess up a part, just remember that you can go back to it in a minute and fix it.
I often do some of my highlighting on the black before I apply yellow paint to the mini. Since you already have a good shaded white area to work from, you'll mostly want to try and get the black highlighted areas to match the white highlighted areas.
The yellow is applied with layers of thinned down yellow paint/ink. The thinning helps it keep the shading that you did with the white, even though you often have to do some of the extreme highlights over again afterward.
Almost every hazard stripe that I've painted is also quite dirty, and battle damaged. You can apply battle damage to hazard stripes the same way as anything else (and if you're damaging the mini, you need to use the same methods or it will look wonky).
As for grime, I usually like to throw on a quick glaze-thin coat of brown, gray or rust colored paint. It is best to use colors that you have on your base (so that we know where the mud has come from) and also to match any grime that you've put on the rest of the mini.
The only other thing you'll need to watch for is placement. Hazard stripes tend to be very bright focal points for the eye, so try and keep your mini balanced. I often do stripes on two opposite sides of a mini to balance it out.
Alright, now go have fun with it.