Faith and funerals go together like hand and glove. You can have a hand without a glove and a glove without a hand, but they are frequently together, and when they are, they usually appear as one. First thing to do, when someone you worked with, or played with, or that you cared about has died is to let go of any notion that you will not attend their funeral service because of a difference in faith.
We live in a world of different religious beliefs. In the course of our life, we connect with and care about people who practice a religion that is different from our own. This does not remove our human connection. Look to your own faith and you will likely see a teaching about doing unto others as you would have them do unto you. Push past your discomfort or fear and do what your heart and your faith tell you is right. Act out of kindness and love.
A good place to begin is to find out what will happen, what you can expect at the service. Google it or call the place of worship where the service will be held and ask. Knowing what to expect will go a long way to calm your discomfort. Understand which, if any, parts of the service you will not be expected to take part in. Also determine if there are any aspects of the service that you prefer not to participate in. You will not be expected to do anything that goes against your own faith.
In some churches the funeral service is just like any other weekly service in that particular faith. The deceased may or may not be eulogized. In some faiths only those who practice that faith will be expected or even allowed to participate in communion or some other aspect of the service. Some will stand, some will kneel, others will sit. Generally, what you do as a person of a different faith is observe respectfully.
You may also find there is more than one opportunity to offer your condolences to the family. If calling hours before or after the religious service are offered, you may find it more comfortable to attend calling hours and skip the religious service.
Finally, go with an open mind and heart. This is an opportunity to learn. You will no doubt learn what your friend believed. It may be more like what you believe than you expected, or it may be very different. In any case, regardless of faith, love is universal. When people experience a death, they like to hear about their loved one. They like to know that you too will miss his or her presence and that you enjoyed time with them, and they were loved and respected by a large circle of friends and colleagues.