What's the best way to remove wrinkles from clean clothing?

Iron them?

If it is something you usually don’t need to iron, just spray with water and smooth with your hands or spray with water and put in a low heat dryer for a few minutes. You can steam the wrinkles out if you have a good steamer, that is one of the best ways.

Ironing? Heck, no!

How about a steam roller.

I heard a steamer is a great thing. I don’t have one but I heard they’re very easy because you just steam them while they’re hanging up. I heard you can also steam curtains and drapes and it’s very easy.

If you are in a hurry, leave the clothes hanging in the bathroom while you take a shower and the steam will do somewhat of a job, but not as good as an iron.

Hang with hanger on shower rod, spritz with water, dry with blow dryer.

Wear a sweater over the wrinkled shirt.

I have a “refresh” cycle on my dryer. I hate ironing. Hate it!

The key word here is best.
That being said, iron.
You apparently do not really want to know about best.
So go for second best.
Any of the above.

After washing & drying the clothes, do iron on it, if possible. Either you may hang it on the hangers so that clothes are away from any wrinkles.

Like @Katniss, we have a refresh cycle. I use a barely damp washcloth and throw it in with whatever needs to be de-wrinkled. 15 minutes usually does the trick.

After looking on the Internet, I put the clothes in the dryer on medium with a damp washcloth for 15 minutes. The wrinkles all disappeared!

Use a steam iron, that’s the simplest way to do that.

Of course, my cloth got re-wrinkled in the suitcase.

A trick for folding clothes for suitcases is to fold it around a t-shirt so it holds it shape better. Also, sometimes rolling a garment is better than more folds and laying flat. The best thing is fabrics that don’t wrinkle easily. Crepe is great for suits. Cotton knits for tops. Blousy tops, polyester can always be wet down and hung to dewrinkle (it rarely wrinkles anyway).

Side note: the women who invented permanent press just died a few days ago. She was in her 90’s I think.

Don’t use dryer to dry your clothes. After wash, fold your clothes as a proper manner. And use, hangers or other things to to hang your clothes.