Half of my disk storage is labelled "other". How does one access "other" in order to free up disk space?

Other is everything that doesn't fit into the rest of the categories. It isn't a location or a single type of item.

So, it is comprised of things that are not Apps, or Music, or Videos, etc.

You can search your disk for things that are not any of the other categories.

Or, you could use a tool designed for the purpose of finding large chunks of storage, like OmniDiskSweeper or DaisyDisk.