Tips to get around in Kuwait 

 
Dress code
 
It is not necessary for women to wear the Abaya (sort of like a Burqa), a Hijab (head scarf) or a niqaab (face cover).
 
Abaya & Hijab 
Shopping postcard
 
Hijab
 
But you should wear long pants and at least a T-Shirt. Loose, not tight.
Some call it respect, some call it peace of mind.
In the end, you will find your own way of dressing, one you feel comfortable with.
People, especially men will stare at you, no matter what you are wearing.
 
For men it's easier. They can actually wear whatever they want as well.
In most travel guides you read that you shouldn't wear Shorts, but actually, it doesn't really matter.
You will not see a Kuwaiti in Shorts (or rarely), but many other people DO wear Shorts here now.
Tank Tops are still a bit frowned at though.
 
Photography
 
It's usually no problem at all to take pictures.
NoNo's are: Taking pictures of people, especially women without their permission, 
Public buildings like the Seif palace and Oil refineries, tankers, etc.
You will find it easy after a while to figure what and what not to shoot.
Most men LOVE to pose for you, well, at least when you are a woman ;)
 
Getting around
 
You can easily use taxis in Kuwait.
They are not overly expensive. Just watch out that they are marked as a taxi.
You can wait at the side of the road and just wave at one that passes by.
Don't accept the first price. Bargain! If the driver says 5 KD, go down to 2 and meet somewhere at 3.
If not you are getting ripped of almost for sure.
They might try it with everyone, but they try it especially with any Westerner ;)
 
You can also use the buses, if you know the time table ;)
There are separate areas for women and men, so you should be able to travel in peace.
 
Rental cars are not overly expensive in Kuwait.
In general, you are allowed to drive when you have an international drivers license and a visitors Visa.
If you have a work Visa you need to get a Kuwaiti drivers license.Women are allowed to drive.
I'm not sure, if I would recommend driving in Kuwait though.
Driving here reminds me of a Formula 1 race.
At least the Police Force is not on the Kuwaiti's side only any more.
They do check nowthesedays who is at fault, even if you are a foreigner.
 
At the markets
 
Don't forget to do some small talk and bargain.
The shop owners love it. It takes a bit to get used to, but it's worth it.
For women: If possible, take a friend or a male companion with you.
You will not get kidnapped or harmed, but men might keep talking to you or follow you.
Many don't take "No" for an answer.
Watch over your wallet and purse.
Don't let your attention drop or someone might take advantage of your money and papers.
 
Temperatures
 
Except for July to end of September the temperatures are bearable.
Those three months though the heat climbs to over 50 degrees Celsius during the day.
 
Working hours and weekends
 
Weekends in Kuwait are since October 2007 on Fridays and Saturdays.
Most shops are open, big Supermarkets are open almost 24/7.
Small shops and Souqs don't open before 10 a.m., most close after 1 p.m. and open again after 4 p.m.