There are quite a few VPN apps available in the Google Play Store, and most of them you can use for free, to a certain degree. Some apps limit you in terms of download / upload speed, others don't allow you to select from which server to connect to, while some flat out request payments.
Having said that, VPN apps can be quite useful, and if you've never used one, we'll simply explain how to do that. Before we start, though, it's worth noting that VPNs can be useful if you're trying to access content that is not allowed in your area, for some reason, as VPN stands for Virtual Private Network.
Once you download and fire up a VPN app, it will mask your phone's connection, as if you were connected from a different place. For example, if you're from the US, you can download a VPN app, select a server from Germany, and to other sites it will seem as if you're from Germany, not the US.
So, if you're in need of such an app, ProPrivacy actually compiled a list of really good VPN applications for Android that may be worth trying out. If you open the provided link, you'll be able to see the pros and cons of five extremely popular applications for Android, and also get some more info about each of those applications.
Once you decide which app you'd like to use, simply install it from the Play Store. Once you do that, run that app, and chances are you will immediately see an option to connect on the display, presuming that the app is not of the paid-only variety. If you hit that "connect" button, you will be connected on a random server, most probably, at least in the vast majority of applications.
Now, most VPN apps offer you a chance to choose a server from which you want to connect, so, for example, if you want to connect from a server in Germany, select that server and that's it. As already mentioned, most VPN applications will either considerably limit download / upload speeds once you manually select a server, or you'll be required to subscribe before you can connect to a specific server.
If you find yourself in need to use a VPN connection often, paying for a service may not be a bad idea, as once you do that, you'll get a lot more options plus full download / upload speeds. So, for example, ExpressVPN app is not the most affordable out there (it costs $6.67 per month), but it offers a 24/7 live chat support, a 30-day money-back guarantee, plus servers in 94 countries, which is above and beyond what most VPN apps offer.
ProPrivacy states that PrivateVPN app is the best value for your money, as it costs only $1.89 per month, and it allows for 6 simultaneous connections, great customer service, strong encryption, and so on. NordVPN is also a good, affordable option, while IPVanish and VyprVPN are good services, but they're a bit more expensive than PrivateVPN and NordVPN. It all depends on what you need, so check out ProPrivacy's list and see what fits you best.