The biggest difference compared to living close to where you grew up applies even to roaming Americans: When you move to a new place you know nobody. How you deal with this situation depends very much on how used you are to meeting new people. If your life revolved around a big extended family this may be a different challenge than if you were a member of different clubs and had friends from all wakes of life. Children are usually very good at approaching strangers and ask if they want to play - adults less so. We have often relied on a network of family, friends from our school days, colleagues from our youth. Now we have to start from scratch.
Because it is really hard to socialize all on your own. The Resources page has links to various multicultural venues and Facebook is also a great source for finding fellow countrymen abroad. I know you probably didn't go abroad to commingle with only people from back home, but, if they have been around for a while, they are great for teaching you the "dos and don'ts". They may have local friends that you will enjoy meeting and they will let you know in which club or church they feel comfortable. In short, they may better than many other understand "where you come from".
Even if you don't expect to stay for more than a couple of years on a transfer assignment, announcing that you almost have a foot out of the door already is not conductive for making new friends. It is hard to lose friends when they travel to a new post or back to the old country and some people may keep a distance if they think their friendship efforts will be "wasted" on you. Assume - at least publicly - that you will prolong your contract and stay forever. Who knows, perhaps you will?
If you are relocating alone - without a family - ask your new colleagues what they do after work. Can they recommend clubs or hang out places? What do they do on weekends? You can not only get advice, you have also signaled that you are open for making new friends. They may offer up themselves but might not have thought of that if you hadn't opened up first. Remember, we are all afraid of getting rejected. You are foreign and by that mark both interesting and a little dangerous. Let us hope your colleagues are curious.
If you are a family, one way to reach out is to arrange a back yard BBQ once you have unpacked your new home. Chance is, that your new neighbors are just as curious about you as you are about them. They may even have swung by and introduced themselves. As much entertainment can be arranged outside - the weather is pretty reliable around here all summer and fall and people are used to potluck parties - it can be done fairly easily even if you invite many. Ask people to bring what they want to drink and a side dish, then you will cook hamburgers and hot dogs (or chicken or lamb or fish or whatever is your taste), and be open about that you are interested in meeting new people as you are "the new kid on the block". Chance is that somebody will invite you to join their church, sports club, walking group, book group... If you have kids, you will know who have teenagers eager to babysit, who have kids for your children to play with. And it will be easier for other parents to feel safe about letting their children play at your house, if they themselves have been inside and seen that you are not some deranged person who will eat their little ones for breakfast.
If you invite new people to a home cooked meal - even in the back yard - it is prudent to ask if there are any dietary restrictions. Because of the ethnic diversity of the Valley there are preferences avoiding cow or pork - or meat in general - and scaringly many have food allergies, particularly to peanuts or nuts in general. Peanut butter has been a stable in the American kitchen, being both nutritious and cheap and not spoiling in a lunchbox, but has left many allergic. Inviting people inside for dinner is not very common. Much entertainment is done either by going to a restaurant together or as one of the aforementioned BBQs, either at home, as a block party, or gathering in a park where iron BBQ boxes await your charcoals.
With the different preferences for various foods, buffet serving is more common than sit down dinners. This not only give people a chance to chose according to their preferences, it also makes the whole affair less formal and thus ties better with the fact that nobody arrives at a given time and many leave early. Perhaps to go to another event afterwards. And American hosts are just as frustrated about this as you may be.
Attire in California is very laid back most of the time. With the exception of weddings and proms, the dressed up look is what in Europe is referred to as "country casual". Otherwise jeans and a t-shirt with a sweatshirt in the car is common for an evening BBQ outing, shorts and T ok for an afternoon event. No harm done in asking your hosts.
Do take this seriously. Homo Sapiens is a social species that gets depressed if it doesn't have a large enough tribe to roam with. Friends are a necessity, not a luxury.