TimeTraces shows you current information on the project in the main window. You can choose to see the worked time per hour, per day, per week, per month, per year and for the project as a whole; you can switch between these reporting modes by selecting the desired mode in the "View" main menu. TimeTraces will show you two "per day" columns by default, but you can change the number of columns in the "Settings" window (select "Options \ Edit settings..." from the menu).
When the option "Follow current date/time" is chosen in the main window, TimeTraces will make sure that the last column displays the current date or time. When you want to see other dates or times in the columns, select the option "Show date/time", and then browse to the desired date or time using the browse buttons.
To see the overall current totals for the whole project, you can open the "Project statistics" window via the menu item "Project \ Statistics...". This window will tell you the total amount of hours registered on the project, the start- and end date of the time registration, and some information about the project.