The simplest way to connect to eduroam is to make use of the geteduroam app. The geteduroam app takes care of all the fiddly settings, allowing you to simply select your home institution and then enter your username and password.
Find geteduroam in your device's app store, install it, and then follow the instructions
If you're using a supported device, you can usually find the necessary installer from eduroam CAT. Head on over to https://cat.eduroam.org/ and click on the "Click here to download your eduroamĀ® installer" button to find the right installer for you.
Unfortunately, devices declared end-of-life by the manufacturer or are out of general support (e.g. Windows XP, 7) aren't supported. This is partly because of known security concerns - your password would be at risk - that there's no way to work around.
Please don't be tempted to guess or enter details manually. It might seem like this works, but it is very easy to make a mistake that weakens your security and allows people to steal your credentials. And for this reason, it's sometimes not possible to do this on newer versions of Android or Windows.
Your institution may have a web page where they provide the correct info. If so, you might be able to find them by clicking the button below.
All of the above methods depend on your home institution telling eduroam the correct settings for their servers. If they've not yet done this, then you won't be able to use geteduroam or eduroam CAT (your institution simply won't be listed). If that's the case, get hold of your home institution's IT help desk and ask them to configure this for you!