Ethos is an appeal to authority. Speakers use ethos when they either mention their own authority on a subject or reference another authority when citing claims. For example, if a speaker were trying to convince their audience that they should not smoke tobacco, they might quote medical experts on how the habit is detrimental to one's health. The medical experts clearly know what they are talking about, more so than the average person. Their credentials make the listeners more likely to take what they have to say seriously.
Pathos is an appeal to emotion. The speaker may want to make the audience feel a certain way to make them more open to what they're trying to argue. For example, if a speaker were giving a speech on why they believe meat-eating is immoral, they might refer to the appalling conditions of slaughterhouses, appealing to the sympathy of the audience and gearing for a gut reaction.
Logos is an appeal to logic. Logic-based appeals tend to be in the form of figures, statistics, and straight facts. Going back to the anti-tobacco speech example, the speaker would be using logos if they cited the number of tobacco-related deaths in the United States on average every year. Since it is such a risky habit, logically it would be sound to avoid it.