The WHO website has some good information about Ebola. In particular,
Ebola then spreads in the community through human-to-human transmission, with infection resulting from direct contact (through broken skin or mucous membranes) with the blood, secretions, organs or other bodily fluids of infected people, and indirect contact with environments contaminated with such fluids. Burial ceremonies in which mourners have direct contact with the body of the deceased person can also play a role in the transmission of Ebola. Men who have recovered from the disease can still transmit the virus through their semen for up to 7 weeks after recovery from illness.
Health-care workers have frequently been infected while treating patients with suspected or confirmed EVD. This has occurred through close contact with patients when infection control precautions are not strictly practiced.
and a little later on
It is not always possible to identify patients with EBV early because initial symptoms may be non-specific. For this reason, it is important that health-care workers apply standard precautions consistently with all patients – regardless of their diagnosis – in all work practices at all times. These include basic hand hygiene, respiratory hygiene, the use of personal protective equipment (according to the risk of splashes or other contact with infected materials), safe injection practices and safe burial practices.
Health-care workers caring for patients with suspected or confirmed Ebola virus should apply, in addition to standard precautions, other infection control measures to avoid any exposure to the patient’s blood and body fluids and direct unprotected contact with the possibly contaminated environment. When in close contact (within 1 metre) of patients with EBV, health-care workers should wear face protection (a face shield or a medical mask and goggles), a clean, non-sterile long-sleeved gown, and gloves (sterile gloves for some procedures).
News articles have also reported other important information:
The spread of the disease is worsened by mistrust of western medicine in some African communities
Some believe the outbreak is a hoax - or even that health workers are killing patients.
But Dr Walsh says any cases that reached Britain would be far more manageable. He says: “Ebola is pretty containable with modern methods in modern countries. You won’t see a major outbreak in the UK.”
In summary, Ebola is scary because it has the potential to become a pandemic that kills millions or even billions of people as it can spread easily from person to person. However, it can only spread through direct contact. If people know this, then it is easy to prevent it from spreading.
The reason it has spread so much already is, as news articles have reported, that the people of the region do not believe what they are being told. That means they continue to engage in unsafe behaviors, such as burial rituals in which they touch the body of someone who died of Ebola.
If anyone in the US was diagnosed with Ebola then there would be quarantines put in place to completely isolate everyone who had come in contact with the person diagnosed. Also, anyone who began to show any symptoms of being sick would immediately be quarantined and tested for Ebola. Ebola is not contagious before symptoms begin to show, so these measures would effectively prevent any further spread.
From another news article:
Symptoms include fever, headache, diarrhea and vomiting. Some patients have trouble breathing.
Doctors are asking patients with these symptoms if they have traveled recently to the three countries primarily affected by the Ebola outbreak: Guinea, Sierra Leone and Liberia. They're also asking if patients have been in contact with anyone else who has traveled to the region lately.
[Dr. Eric Legome, chief of emergency medicine at Kings County Hospital in New York] said hospitals have a low threshold to isolate patients, meaning anyone who is even remotely suspected of being infected will immediately be put in an isolated ICU room so health officials can run tests.
Also, this article does a decent job of explaining how containing Ebola has about as much to do with sociology as it is does epidemiology.
We now have a case of a man being diagnosed with Ebola while being in the United States, and he has just died. Because he was showing symptoms for multiple days before being diagnosed and quarantined, it is possible that he infected some of the people that he came in contact with. Within Ebola's incubation period of 21 days (October 29th, 2014), if anyone was infected they will begin showing symptoms. 21 days after those people recover (late November 2014) we will be able to know if those people infected any additional people. This will give us a good idea of how well the US healthcare system is able to handle Ebola, at least for small numbers of people infected.
Update (Oct 20th):
As of today 43 people are no longer being monitored, including the family of the man who died. Two nurses who took care of him were infected and are being treated. Within about 21 days we will know whether or not there will be any additional infections.
Also, Nigeria has been declared free of Ebola. That article also mentions that Nigeria "has a robust health care system" already and did a good job of tracking the "nearly 900 people who were potentially exposed to Ebola". As a result, there were only 20 confirmed cases of Ebola in Nigeria.
If you read articles about what is being done in the United States, you'll frequently see them mention that the people who were exposed to Ebola are being monitored, such as the 43 people who are now known to not be infected. This suggests that the U.S. is doing a good job of containing Ebola, further strengthening the claim that the disease poses "little risk to the U.S. general population".
Update (Nov 6th):
There have been no additional infections from the case in Dallas. As of today, there is only one person who is still being monitored, and tomorrow will pass the maximum incubation period of Ebola.
The cases of Ebola in Texas have given us what we previously lacked - evidence of whether or not an outbreak could be prevented. Even though Thomas Duncan (the man who died) was not quarantined while he was symptomatic, not a single member of the general public was infected by him or by the two nurses he did infect.
If you'd like to read a humorous article about why we don't need to worry, Cracked just did an article on it.