There's a ton of information out there on what the pros do to keep a perfect finish, but mostly, it boils down to:
Washing should be done with automotive shampoos only. I know a lot of guys will say, "Dawn or other detergeants are just fine..used 'em for years...never a problem...etc", and maybe they're right. What I do know is that dish detergeant is made to strip everything off the surface, including the wax, and according to Dawn's site, should not be used for automotive paint because it can strip polymers from the paint surface and accelerate the oxidation process. I figure if the manufacturer is issuing the warning, I'm gonna listen. That said, do what you want. How you wash your bike dosn't affect me, and I have no interest in fighting a religious war
The reason you should wash before any of the other steps is to remove as much dirt as possible to minimize the possiblity of creating more micro-abrasions in the clear coat. Let everything dry, and then move on to the next step. You'll be removing any watermarks soon enough.
Polishing and waxing are two different things. Polishing is the exercise is removing blemishes and smoothing the clear coat to remove all micro-abrasions. This preps the surface for waxing. Some people will tell you that polishing is removing the top layer of the clear coat and some will claim that it's filling in the gaps and cracks in the clear coat. They're both right. To remove real blemishes (i.e. cracks a marks that you can feel), you'll need to use rubbing compound. This will remove some of the clear coat to even the surface and eliminate the mark(s). I use the finest (as opposed to coarsest) compound I can find. Be careful with rubbing compound, it can do some damage if you're not careful. Using other polishing solutions (Mother's), that are not rubbing compounds, both takes off a tiny bit of clear coat and fills in the cracks to eliminate swirl marks and those super fine abrasions you see in the paint. Contrary to popular belief, both polishes and waxes should be applied in a "back and forth" motion rather than in circles. Pick one...front/back or side/side and stick with it. Don't mix and match. It may take some pressure when using compound or other polishes to get perfect results.
At this point, you should have a perfect surface, and you're ready to protect it. Time to add the wax. Some people prefer the carnauba wax paste and some like the liquid. The only difference I've seen is that the paste tends to be natural, and the liquid tends to be the engineered carnauba. Personally, I think the liquid looks just as good and lasts longer. Again, do not apply this in circles. Little to no pressure is needed when applying or removing the wax.
Beyond this, I'd recommend only using 100% cotton cloth on paint for washing, polishing, and waxing. Some people prefer microfiber for the latter two steps, but I stick with cotton. For engine parts, wheels, etc...I use soft sponges... and brushes on the wheels and tires as needed. Chrome is another animal, and I'm tired of writing, so maybe I'll add more later.
Disclaimer: I am not a professional (at this anyway...I'm a computer jockey
. Take this for what it's worth (remember you got this info for free). This is how I do it with some success. If you have a different process that you swear is better, I'll forstall the argument by saying up front, "you're probably right." I take no responsibility for any damage you do to your bike by following my process (meaning, if you crank down too hard and long on the rubbing compound and screw up your paint job, it's on you).
Otherwise, I hope this helps you put a perfect finish on your bike!