Connection issues are usually caused by your phone settings, or problems with your Internet connection or mobile provider. In most cases, Internet connection problems are temporary and your messages will be sent and received as soon as you move to a place with a stronger signal.
If the steps above do not help, your mobile provider may be blocking the specific data channel that WhatsApp uses to send and receive messages. In this case, call your mobile provider and ask for steps to unblock non-HTTP/non-web socket connections. They may be able to help you configure your phone.
It's also important to consider that sometimes messages take a while to send and receive. There are many reasons a message might take a while to be delivered to the other person and only display a single check mark. For example: your friend's phone may not have any data credits left, coverage, or their phone may be turned off.