I need to mate two parts together but they were created in different files. How do I bring the parts together into one file?
Copy from one and paste to the other, is the most basic way. Or you can import one into the other, or save one as a component and bring it in from the component browser.
And note that the Paste in Place function can be very handy to preserve the original position and orientation of an object that was copied from one file and is to be inserted into another file.
If you’re using the web version as indicated by your profile, you won’t be able to copy and paste from one SketchUp file to the other. You’ll need to save the part as an SKP file and then, in the other file, insert the saved part using File>Insert.