The installation instructions (also for other OSes) are at https://www.wireguard.com/install/

As i have Ubuntu VPS server, i used command:

# sudo add-apt-repository ppa:wireguard/wireguard
sudo: add-apt-repository: command not found
So i heard that missing package is in following package (20MB additional data):
# sudo apt-get install software-properties-common

Result:
E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?
# apt-get update
E: The method driver /usr/lib/apt/methods/https could not be found.
N: Is the package apt-transport-https installed?
E: Failed to fetch https://deb.torproject.org/torprojec...nial/InRelease
E: Some index files failed to download. They have been ignored, or old ones used instead.
# sudo apt-get install apt-transport-https -y;sudo apt-get clean all;sudo apt-get update;software-properties-common -y

That worked. So again i try to add WireGuard ppa:

# sudo add-apt-repository ppa:wireguard/wireguard

Finished OK. I proceed with installation instructions:
# sudo apt-get update;sudo apt-get install wireguard
(it added around +100MB of disk space.)

It said: Configuring libc6 ; Kernel version not supported
and that it supports version 3.2 and later
OK

then it continued and finished with messages:

Loading new wireguard-0.0.20181218 DKMS files...
First Installation: checking all kernels...
dpkg: warning: version '*-*' has bad syntax: version number does not start with digit
It is likely that 2.6.32-042stab125.5 belongs to a chroot's host
Module build for the currently running kernel was skipped since the
kernel source for this kernel does not seem to be installed.
# wg
command does nothing

# service wg status
* wg.service
Loaded: not-found (Reason: No such file or directory)
Active: inactive (dead)
No work around if i can not get newer kernel?