I'm so sorry you are going through this with your father. I just want to give you a great big virtual (((hug))).
Others have offered great advice, but I especially wanted to emphasize EJ's: focus on just spending time with your dad and listening to him talk about his life. Talk to him about his fondest memories of childhood and adolescence, and let him share funny stories. Go through photo albums together; this will spark recollections. If you have loose photos of him and your family, consider placing them in a photo album to surprise him with, and then spend time looking through it with him.
I love the idea of recording his voice and your conversations together (with his knowledge and permission, of course). You might want to consider videotaping some discussions, too. The memories he shares with you will become warm words of comfort for you for the rest of your life. What he shares with you will not go to the grave with him, but instead, part of his essence in the form of his life memories will be passed along to you to hold dear. This experience will also provide your father a warm validation of his life: someone loves and cares for him enough to just sit and reminisce with him about his life.
Don't forget about the present though: focus on the things that bring him pleasure, if even fleetingly. If he has an appetite at all right now (which he may not), surprise him with a treat you know he likes, for example. Play an album by a band that you know he liked when he was in high school; don't mention that you got the album ahead of time, but just play it in the background when you are visiting with him. Take the time to just sit and watch the sunset or sunrise together. It's the little things in life that make each day worth living, particularly when the person knows s/he is definitely living out his/her final days. Those little things suddenly become the most important things--and loving someone who is terminally ill also helps you refocus on what is most important.
We are all here for just a short while in the grand scheme of things, but that just makes each moment we live so very precious. Let this experience help you to value each of your own moments even more and to treasure everyone around you just a bit more. Learn to be more gentle and forgiving of your own shortcomings and the shortcomings of others.
And just realize that it is perfectly normal to feel overwhelmed by grief. Never hesitate to reach out to others when you need to vent your feelings, whatever they may be. Just know that you have the internal strength to get through this, no matter how difficult and painful it may be.