In general one should use layout managers for this purpose. That what they are designed for.
Delphi (did not work with it for a long time) does not have such managers but is able to handle different dpi ever since. You have to use the autosize propery of the components to ensure that they have the right size for the text they display. To prevent overlapping of components arrange them on the form using the alignment and anchor properties. Eventually you have to group components in containers to achieve a proper layout.