There are a couple ways of doing this.
Either you ask them to transfer ownership to you or you make copies of the files.
The first step is to understand how to search drive for files "by owner" - you use the advanced search in drive (click the toggles icon in the search bar)
Make copies of files
If you want to make copies of the files search for "not owned by me". Right click on the file you want to copy, select file information and show location ( if you don’t do this and go to the folder where the files are, the copies get put into the root folder of the drive - i.e. the copies won’t be in the right place ). Select all the files you want here, then you can right click and select make a copy. Once you have confirmation that the copies are made, delete the files you have selected. Be aware that this will break any shared links for the files you are deleting. There is a useful bulk rename utility that will help you delete the "Copy of" that appears in all the names of the recently copied files.
Transfer Ownership
Only the person who owns the files can initiate transfer of ownership. That person would have to search for "owned by me" and select the location of your drive. They can select all the items and then use the share dialogue to change your access from editor to "transfer ownership". This works a bit differently depending on whether your drive is a personal account / they have a personal account or if you both are in the same workspace / organisation. It won't work if you are in different organisations - use copy in that case.