Home is where you lay your head at night. When starting over in a new location it is important not to get too wrapped up in all of the things that you do not yet know about your new area. This can lead to becoming quickly overwhelmed and homesick. Remember that this is an adventure and you are in your new home.
Ensure that you have all of the vitals in place: a place to live, food to eat, communications, and an income. Your place to live can be a rented room or a bare apartment. As long as it has a roof and a door, it can be yours and you can be happy there. If you are starting off on your own for the very first time, you might not have much in the way of material possessions. That's okay. If it's your first day in town and you don't have the time or the resources to fully outfit your new place, get a cheap air mattress and some bedding and call it a day. When you have a little more time (and cash!), purchase the furniture that you'll need to feel comfortable in your new home.
Once your place to stay is set up make sure that you stock the fridge. Nothing is worse than dealing with the culture shock of life in a new city and not being able to comfort yourself with healthy, familiar food. Find the local grocery store and get your favorites stocked in the kitchen.
You'll likely find yourself very lost more than once while navigating your way through this new area. Don't fret. Getting lost is actually a really great way to learn your way around a city. Keep a map with you and use it often. Make sure that you also have a means of communication available in case you get yourself into a bind and need to call roadside assistance or the like. A cell phone is ideal, but if you cannot get a cell phone then at least keep a calling card with you.
In an ideal world, you will be relocating with a job in place. If, however, you do not have a job in your new city then this should become your first priority. Find the local paper and search the classified ads. While you're looking for a newspaper, make sure that you strike up a friendly conversation with everyone you meet such as the store clerk and your bus driver. If you appear to be friendly and polite, these people are more likely to assist you when possible and might even drop you some hints of places to look for work. Making friends, and not enemies, is the key to starting off in a new city on the right foot.