Many people use the term “custody,” but custody is not actually a term you would find in a Texas order. The order will discuss conservatorship (rights and duties) and possession and access (the schedule). When most people say “custody,” they are thinking about the schedule.
A large number of custody arrangements involve a standard possession order. With a standard possession order, the noncustodial parent (the parent who does not have primary custody) would have the child for the first, third and fifth weekends of the month (usually from Friday at 6 pm until Sunday at 6 pm), one evening during each week (usually from 6-8 pm), every other holiday and thirty days in the summer (42 days if the parties live more than 100 miles apart).
Now many families opt for an “expanded standard possession order,” which gives the noncustodial parent the first, third and fifth weekends from Friday after school through Monday morning and every Thursday overnight. It includes the same holidays and summer schedule as above.
Some families opt for a true 50/50 possession schedule, with each parent having the children half of the time. Some people choose a week on, week off schedule. Others split the week such that one parent has Monday and Tuesday, another has Wednesday and Thursday, and they alternate weekends.
If the parties are going to agree, they can basically choose any possession schedule that works for their family and a judge will approve it. If the parties are not going to agree, my experience is that most judges will opt for either a standard possession order or an expanded standard possession order.