When you open a project plan it opens at the start of the project. This can be frustrating to have to scroll to the right to get to today's date.
One way to resolve this is to find a task that is happening at the moment and click on the "Scroll to Task" button.
Finding such a task is easier if you apply the standard filter "incomplete tasks" as this hides all the activities which have been completed.
However, sometimes this isn't enough.
For these times you can use the following very simple macro:
Sub Goto_today()
EditGoTo Date:=Now
End Sub
To enter this press <ALT><F11> to get into the VBA editor. Here you can choose to apply the macro at the ProjectGlobal level or limit it to your current plan.
To make it easy to access the macro you can add it to the Ribbon.
if you don't like the standard button you can select a new image by selecting "rename" from the right mouse button when adding the macro to the ribbon
If you want this to always happen when you open a plan, you can arrange for the macro to be run at startup as shown in this Microsoft post:
Update:
The manual method to do this, which is arguably faster is to hit F5 (usually used to jump to a row in the plan), then Tab to move to the date section and then enter Today