"My ex drops our son off at day care Monday morning and I pick him up Monday afternoon. I drop him off and pick him up from daycare on Tuesday, and then I drop him off at daycare on Wednesday, where my ex picks him up in the afternoon, and so on. How do I track this?"
You would keep track of this the same way you would keep track of any other time period- simply record the appropriate start and stop times, as often as necessary. The child is normally either with one of you or is in daycare. When he is with you, record the time. When he isn't with you, don't record any time.
The exception is NP Time, which is time when the child isn't with either of you (such as with time he is in daycare).
In the example above, you would set a start time for when you pick the child up on Monday from daycare, and a stop time on Wednesday when you drop him/her off. For Monday, Tuesday, and Wednesday, you'd also record the appropriate NP Time. If the child is in daycare when your ex has custody, be sure to note NP Time for those days as well.
In short, make as many start/stop periods as necessary to show where the child is and who he is with.