When I'm at work, I have a one cup coffee maker that I keep on my desk. For tea, I usually use the hot water from the lunch room. Most places I've worked at either have a water cooler that has a hot water spigot or a coffee maker that has a hot water spigot.
At home, I use my mom's coffee maker or I put the kettle on for hot water. Sometimes, I heat water up in the microwave and add instant coffee or a tea bag after the water is hot.