Most of us just don't know what to do when someone is seriously ill. We want to help. We feel weird and awkward and scared. So: if you have a friend in this situation, what can you do?
Saying "Let me know if I can do anything" to your friend or your friend's caretaker is not actually helpful. Offering to do specific things is very helpful. You could ask, "How about I come over this afternoon and fold some laundry?" or "I'm heading to the store; what's on your grocery list?" or "I'm free to run errands or take the patient to doctor's appointments on Wednesdays." Offer to coordinate other offers for help or meals, or to help spread news of the patient's condition.
Just because your offers of help are sometimes turned down, don't be discouraged or deterred. Continue to make specific offers of help from time to time. Things change constantly in the life of someone dealing with a serious illness. Don't be offended if your offers are declined. Keep offering (without turning into a stalker!). Realize that it may be incredibly difficult for your friend to accept your help. It means acknowledging that your help is now needed. Don't make comments about being upset when you hear others have been asked to help and you haven't. Patients and caretakers probably don't have the time, energy, or emotional bandwidth to worry about everyone else's feelings.
You don't have to offer help. Just keep communicating as usual. Send emails. Send the kind of emails you used to send before your friend became ill. You don't need to treat the illness like an elephant in the room; simply acknowledge that you're thinking of them as they deal with the sickness, then move on to normal topics. Send cards. Send pictures drawn by children. Let them know you're praying for them or thinking of them. Post funny stories on their FB wall. Send a text that says "Hi, thinking of you and sending love." Gestures don't have to be grand. Understand that you may not get a prompt reply, or any reply at all. That does not mean your message wasn't appreciated.
Often, people who want to help friends dealing with an illness will think of preparing meals. This is not always as helpful as you might think. Please don't just show up with a large casserole. Ask before you bring food. It might not be needed; it might create another problem that your friend doesn't have time to deal with. Find out if the patient has any dietary restrictions and prepare the food you bring accordingly. Pack food in disposable containers (individual-sized containers are helpful), and label the containers with the contents. Don't ask later if they liked the dish. Try to remember that days and meals tend to blur together. Again, just because your contribution was not acknowledged does not mean it wasn't appreciated.
Find out if a visit is okay before you drop by; when you ask, make it clear you understand if they aren't up for visitors. When you do visit or call, talk about what your kids are doing in school or the latest political crap at the office or whatever is "normal life." Hearing about normal life—anything that's not related to the illness—can be highly encouraging. Keep your calls or visits short. You don't have to wait for the normal social cues to leave; just watch the clock and make excuses about being busy and leave after 20 minutes. Do not be offended by last-minute cancellations.
Remember that the patient and the patient's caretakers don't know how to do this either. They were living their lives, and they suddenly found those lives transformed into a crazy, terrifying odyssey. Now they're trying to figure things out as they go. Allow them plenty of room for making mistakes in their plans, their schedules, their expectations, and their feelings. Rants, emotional outbursts or unusual silences can and probably will happen. All the rules in their lives have changed, and they will need plenty of patience and understanding from their friends for the mistakes they will most certainly make.
Realize that you will feel some difficult and uncomfortable emotions over your friend's illness. It's important to acknowledge that the illness will affect you, too. (Just don't acknowledge this while you're visiting your sick friend!) It may drain you to see the patient looking poorly, or to see the caretaker so obviously stressed. Understand that it's okay to be freaked out, pissed off, scared, worried and relieved it's not you. It's just not okay to express these feelings to the person who is ill or to their caretakers. So make sure you take care to process your emotions properly. Don't bottle up your feelings. Do this for yourself, and so that you can be as available and supportive as possible to your sick friend.