Install open-vm-tools and run:

sudo mount -t fuse.vmhgfs-fuse .host:/ /mnt/hgfs -o allow_other

(Make sure /mnt/hgfs exists and is empty)

You can put configuration stanzas in /etc/fstab to facilitate this, and then mount /mnt/hgfs will work.

See the Setting up auto-mounting section for setting up auto-mounting instead.

Pre-work

Make sure open-vm-tools (and open-vm-tools-desktop if you’re using a desktop environment) are installed, and that you’ve rebooted after their installation.

sudo apt update
sudo apt install open-vm-tools open-vm-tools-desktop

Make sure you have a /mnt/hgfs directory made and empty. If not:

sudo mkdir -p /mnt/hgfs

Mounting

To mount the filesystem, run:

sudo mount -t fuse.vmhgfs-fuse .host:/ /mnt/hgfs -o allow_other

The shared folders will now be in subdirectories of /mnt/hgfs

Setting up auto-mounting

Add the following line to /etc/fstab:

.host:/	/mnt/hgfs	fuse.vmhgfs-fuse	auto,allow_other	0	0

Update: based on extensive testing, the auto keyword seems to work fine. Prior versions suggested noauto. If you have trouble with auto, change to noauto and see below