Start by installing necessary packages:
apt-get install nfs-kernel-server qemu-kvm libvirt-daemon libvirt-daemon-system virtinst bridge-utils vagrant-libvirt
Create an ordinary user and add it to the sudo and the libvirt group:
adduser mike usermod -G libvirt,sudo mike
Now you should be able to switch into this user and give Vagrant a spin:
su - mike mkdir testmachine cd testmachine vagrant init debian/stretch64 vagrant up