Kettles And Cups
There are two main items used in the preparation of tea.
The Kettle must be used to heat water up. It can be filled up with bottles, or with water in your world.
Many mods' alternative water sources are already supported, such as Cooking for Blockheads' Sink, but if you find any that isn't, consider posting an Issue.
To boil to water, you must place the Kettle on a
Magma Block, a
Campfire or any 

Furnace that is currently burning.
Alternatively, a Cooking for Blockheads' Stove may be used as a heat source
Once a substantial amount of steam is coming out, and a bubbly sound is heard, it's ready!
You can now use the Kettle on a Cup.
The Kettle can be picked up by breaking it or right-clicking it with an empty hand or while sneaking.
If you have Simply Tea installed, you may also use a
Teapot from the mod instead of a Kettle
If you use a Kettle on a cow, you can fill it up with milk. This Milkful Kettle can then be heated up just like boiling water to get a Frothing Kettle, used in Lattes!
The Cup is where you put the ingredients for your tea, by placing the cup into the world and using the item on it. Once the ingredient is in, just pour some water from a Kettle to finish your tea!
If you have Simply Tea installed, you may also shift-right click with a
Cup from the mod to place it down

For all the ingredients that can be used to make tea, check Teas.
The Cup can be picked up by right-clicking it with an empty hand or while sneaking.
Kettle
Teapot from the mod instead of a Kettle
Frothing Kettle
Cup
Cup from the mod to place it down