One of the essential questions for women who want to travel Iran is probably how to pack and what cloths are allowed to wear and what not. Fours seasons in one country, Islamic rules and a society which loves beauty and fashion - that doesn't seems easy, but in fact it is. not hard and it doesn't make you ugly.
The main part is to cover the hair with a hijab (headscarf) and to wear the so called manto, a coat which covers as a minimum arms and hips.
Not so important are the ankles. Many Iranian women wear skinny jeans with free ankles and ballerina-shoes. Moreover Iranian women mostly wear their clothes very tight, specially the mantos are worn in tight sizes.
Also all kind of dresses are accepted - Even as a replacement of the manto, as long they cover hips and arms. This becomes handy specially in the hot areas where women in burqa easily get dizzy of the heat (up to 50°C) - what I did: I basically dressed as naked as possible under a dress/Manto and Hijab.
Most often the Chador is used by women, because it seems much easier to put on and off. Although walking and using the toilet was to be the hardest for me with a chador - I guess you get used to it. As a tourist you probably only need the Chador when you want to visit mosques and then you still find some in the entrance.
Burqas are a more extrem case, which is still used, but you don't see very often women covering their entire face. If women wears the black burqa they mostly tie it under the nose, not above it, which makes it a little it funny to look at. Nearly no women wears the Niqab, which is a Burqa which also covers the eyes with a net and is in common use in United Emirates.
In the south of Iran you will find more facial burkas than in the north. The southern burka looks like a mask, which is tied above the chador. The south of Iran is close to the Arabic culture and also to the Indian. So you will find a lot of colors as well as more burqas. Nevertheless Iran generally is a very modern country and you mainly will find girls in manto and a light hijab - which may accidentally falls off from time to time. - So as a tourist you don't have anything to worry about if that happens to you.
Gerally women supposed to cover up inside and outside - either in Burqa, Chador or Manto (Niqab is not common and also not tolerated as a "good thing", because you can't see the face). Most of the families don't cover at home though, as soon as the doors are closed they run around than any other person in Europe, officially this is forbidden.
The fear of being caught strongly depends on the area. Generally it seems the north is not as strict as the south. But Mashhad in the north east is called as one of the most religious cites and lies also in the north. Kurdish-Iran in the west of Iran seems extremely secure and independent, while you find a lot more burqas in the south. But then again controls happening differently from city to city. Smaller cities like Hamedan in the north west have stronger controls on the dress code than Tehran or BandarAbbas in the south, where this is nearly not happening anymore.
For men exist no rules of dressing, although you won't find many men in shorts and T-shirt. And you will find nearly none in a hipster-shirt showing nipples. There are some boys I have met who had to cut their hair, if it was too long or too outstanding. In fact dressing for outside is just about not to stand out, just not to get in trouble.
Still fashion is important. Also for men.
In the Iran Kurdish area you will find nearly all men in Kurdish pants. Those are really loose pants which are quite comfortable. The entire tratditional way of Kurdish clothing includes a belt and a vest and is still seen very often on the streets there.
Kurdish women also dress a little different. Their dresses are transparent with long arms and normally in very bright colors. They wear it with clourful tides or trousers underneath. The head is covered by a kind of hat, which is now, under Islamic control, also is covered by an extra Hijab. Normally the hat is tied with a scarf depending on the relation ship status of the women.
For me as a tourist it was ok to decide my style of hijab depending on the weather. Moreover it is accepted to go outside when the hair is covered with nothing else than an ordenary hat.