Reclaiming Actual Physical Disk Space

I look after a team of DBAs and I have a request to free up space on our very expensive storage system. However the answers on how to do this differ and i'd like to ask for external input...So not being a techincal person I see the world as quite black and white. Meaning that you delete data and you free space but after doing much reading I understand this is not the case, as you essentially create data fragmentation within the datafile resulting in the db having lots more space to write into but not actually freeing space, even if you shrink the file it doesnt free space or do a reorg?

We have as an example a DB with 2 billion rows of data in 1 table, no partioning just one large table. We have worked out that we can probably delete 1 billion rows or even better only keep a rolling 3 month window of data. What would be the suggestion on deleting this data and reclaiming the disk space to actually see additional disk space made available at the os level.

How about deleting the data and reclaiming the space. Through reading it looks like it might be something like, delete, creating new table space partitions from this data. This in theory would create new a tablespace in newly created data files which would result in the data being reorganised and taking up less physical space and when completed you point to the newly created partitions and drop the old tables.

how they have done this as it must be a common problem that people have created some different solutions. What commands, procedures have been used?