The code is regularly reviewed by the community and if vulnerabilities are found, they are fixed.
Besides its age, one of the main reasons why it's trusted so often is that it's open source. OpenVPN is a VPN protocol, which has been around for over 20 years. The longer a product or service has been around, the more time programmers have had to spot and fix vulnerabilities before they can be exploited. Still, in security circles most experts agree that longevity is best. Initial testing of both these protocols has returned impressive results and there's no reason to think they're unsafe.
Most often this is proprietary, closed source software so you have to take their word for it that there aren't any hidden backdoors or undetected security bugs.
Most VPN providers have software you can download so that you can easily connect to their service from your device.
