Copying and pasting objects between experiments in E-Prime is not yet fully supported, but is a planned feature of E-Prime v2.0 which is currently under development. In v1.x, all objects must be recreated manually from one experiment to the next in order to make one combined file.
However, E-Prime v1.x will allow you to copy an object within the Browser window of one experiment, then open a new experiment and Paste that object into the Browser there. E-Prime does not allow you to have more than one ES file open at a time, so you will have to continuously switch back and forth between the two ES files to copy and paste. Keep in mind that only one object can be copied/pasted at a time. Also keep in mind that this method of copying and pasting is very error-prone, and we do not currently recommend using it.
A safer option is to save a copy of the original experiment, delete unwanted objects from the copy, then use the copy as a template for development of your new experiment. The template will already contain the objects you would otherwise have to recreate.