So there are some weekends that are designated as "silver weekends," and this means that training occurs on these weekends. Unless you have some sort of "once in a lifetime event," such as a wedding, you will not be permitted to leave until probably Saturday afternoon at the earliest (once all training is over). There are usually one or two silver weekends per month.
Other weekends are blue weekends, which means they are free. As a freshman you will be allowed limited passes per month to leave base. Additionally, as a freshman, there is a chance you may be restricted to base depending on your squadron's performance. There is paperwork you can fill out to ensure you can leave base on a specific blue weekend even if you are restricted, but this must be prearranged and there must be a reason (concert, parents in town, etc). However, you will most likely still have to stay within your pass allotment even with paperwork.
Paperwork in either case can be started once basic ends and it's not that difficult to fill out. Plenty of time to worry about that after basic.