Assuming you're working with Control nodes, this is fairly easy. Make sure your root node is a container node, such as PanelContainer. Set the PanelContainer to expand to the full size of the viewport by setting its right and bottom anchor properties to 1 and setting the EXPAND size flags in both directions.
Then you can center other control nodes in that container by making use of the container's children anchor properties. For simple cases, it should be enough to set anchor values of 0.5 for the children.
You can also use the FILL (disable) and SHRINK_CENTER (enable) size flags for the children, for example to center a label.
OTOH, if you are working with 2D nodes, not control nodes, these won't automatically reposition themselves when you resize their parents. You'll need to write some code to reposition your nodes to your liking when you resize something. Again, it's easy if your root node is a control node, since control nodes provide a "resized" signal which you can connect to in order to be notified when the window geometry changes.
You should also check out the Godot manual, there's a chapter on dealing with different screen resolutions that might be helpful to you in case you're mainly worried about the application window being resized.