I have several tabs. There is a date picker on each tab. I need that date to be the same on all tabs no matter what. So, if the user changes the date on Tab 1, then goes to tab 2, the date on tab 2 will have changed also. I have never created an application level item before and I thought that might be the most efficient way to accomplish what I need (by setting that item's value to the date the user selected). My problem is that I don't know how to set the value of the application item and also how to retrieve that value on another tab.
You didn't describe what exactly you're trying to do, but - if each tab represents its own table, why do you keep the same date value in all of them? Doesn't look like a normalized data model. Consider using a single date column (in one - master - table) and use (i.e. reference) it in others (i.e. details).
As of your question: How about creating a global page (i.e. page 0) and having a date picker item on it? You can display it on any other page you want. For example, if you set its value while on tab 1 and then move on to tab 3, you can again modify that value which will be visible on all other pages. Basically, you'd maintain just one item instead of as many as number of tabs involved. (BTW, doesn't that remind you of what I described in the first paragraph?).
Alternatively, create a date picker item on tab 1 page; on all other pages, create a "lookup" (display) item which would simply display what's been selected on tab 1. That's easy to do, just make its source to be an "Item", such as P1_DATE_ITEM.