Here's what will most likely happen when you report to your first permanent duty station:
You'll arrive with your family and stay in temporary family billeting. This is sort of an on-base "hotel" for incoming/outgoing military members and their families. It's a good idea to call billeting as soon as you know what day you are going to arrive to make reservations. You'll also be assigned a "sponsor" before your arrival (you'll get a letter with the name and phone number of your sponsor). A sponsor is a person in your squadron who is assigned to help make your move easier. You can call your sponsor when you know your arrival date, and he/she can make the billeting reservations for you. The cost of on-base family billeting is usually $16 to $20 per night. You can stay in on-base family billeting for a maximum of 30 days (the base can extend this to 60 days, if there is space available).
If you can't get into on-base family billeting, you'll have to rent a motel off-base.
Whether or not you stay in on-base family billeting, or off-base motel, you will continue to receive your authorized housing allowance (and food allowance). Additionally, for the first 10 days following your arrival, you'll receive a special allowance, called TLE (Temporary Lodging Expense). This special allowance reimburses you for everything (meals and lodging), up to $180 per day, per family. After the 10 days is up, you'll have to pay for billeting/motel out of your pocket (although you'll still be receiving your housing allowance and sustenance allowance).
You'll visit the housing office and (if you like), put your name on the on-base family housing list. At this time, they can tell you (approximately) how long it will take before an on-base house becomes available. If an on-base house is not immediately available (or, if you don't want to live on base), you'll visit the off-base housing referral section (which is within the Housing Office). They can give you a list of local rentals that have decided to "list" themselves with the base (you are not obligated to use this list. You are free to find a place not on the list, if you want).
After you find a place that you want to live, you take a copy of the lease (before you sign it) to the housing referral office. They check the lease to make sure it contains a "military clause," (A "military clause" allows you to break the lease in case you have to move due to military orders), and to make sure that the military hasn't put the location on the "off-limits" list (this list are for places that have proven racial discrimination, known drug use, etc.)
If you are living off-base, and your on-base family housing becomes available, the military will hire a moving company to move your property from your off-base rental, to your on-base family housing unit.