Monkey see monkey do ;)
You don’t want to arrive at a new culture, and start enjoying yourself as usual. You want to make sure that you observe how the locals carry on their daily affairs, and it if it doesn’t conflict with your value system or religious believes there is no harm in trying to do things differently. This way you avoid unintentionally insulting your host culture, and perhaps get closer to local people.
As said "When in Rome, do as the Romans do".
Slow your pace
Once you arrive, whether it’s business or pleasure, you want to give yourself ample time and plan to do things at a much slower pace. This gives you time for your learnings curve, and plan for unexpected delays as a result of cultural norms at your new destination.
Open your mind
You will probably experience events, practices, rituals and habits at the new culture where it is strange where you come from, you could be insulted, or taken back by it, but don’t. You want to remind yourself that every culture has its own history, complex social fabric and cultural heritage which is the source of pride for locals, that that you don’t understand yet. And once you give yourself time to understand it, it will make plenty of sense. Remember be accepting and understanding, avoid criticizing anything you see until you understand the logic behind it.
Try things out!
Whether its new food or social events, be sure to immerse yourself with the pleasures and riches of your new destination, this will only get you closer to the people and the environment and help make you have a deeper cultural experience.
Keep an open eye
You want to make sure, you walk around and explore your surroundings without being naïve or too comfortable. You want to be vigilant in the sense that, carry as less items as possible (cash, bags, accessories, etc.) always make sure to always carry your travel documents, two copies of a list of important phone numbers, one digital and one written on a piece of paper. Part of being safe and not falling to any tourist traps or being perceived as a target foreigner is to learn as much as you can about the destination country and familiarize yourself with do’s and don’ts, and more importantly with the geography of the city and where are the areas you should and should not be visiting at different times of the day.