How can I gather data from a text box using a Calc macro?

I have a spreadsheet in Calc. I have placed several text boxes and a button at the top of the sheet. My goal is to take the information that the user inputs in the text boxes then organize it into a list of data. The purpose of the application is to log business expenses into a list that can be easily manipulated to show profit/loss as well as expense categories.

How do I gain access to the information in the textbox?

The way to get entered data from a form controil of type TextBox into a cell (or reversely) is to set the property Linked Cell properly.
If you want in addition to move/copy the data elswhere, this can be done by a macro without any reference to the form controls themselves.
Assunming you have linked three textboxes to the cells A1:A3 of thisSheet, your OK Button (action) can call a Sub like

Sub moveDataToCurrentTargetRange(pEvent)
source = thisSheet.getCellRangeByName("A1:A3")
da = source.getDataArray()
target = getCurrentTargetRange(neededParameters) REM (3 rows, one column)
REM Calling a function creating the cellrange to be used to current conditions.
End Sub. 

Details depend on details.

That works for the text boxes. I also have a date and currency text boxes. They do not show that option in the properties window. I there a work around for that?

You may use a TextBox for any entry. To leave the interpretation of the entered text to a macro or to formulas may be simpler than what you originally asked for. That’s because what you had in mind requires to organize the pairing of any form control with its target cell.
Basically form controls are made for usage with database connections.
If you think you need to use form controls not having the Linked Cell property, you may do the pairing by anchoring the control to a cell, and using that cell also for an implicit linkage…
There are disadvantages, however.
If you actually want to do things that way, you will neef to study the usage of the LibreOffice API.