Honestly depending on the tea I brew grandpa style slightly differently. But the end goal the same is, to have as many leaves as possible on the bottom of the drinking vessel to allow for easy sipping, while establishing a strong root. The trick to getting the leaves to stay on the bottom of the cup/bowl is actually very hot or near boiling water, which depending on the type of tea sounds like it could be a bit scary. But I take this as a chance to establish a strong root, while also getting the leaves to be settled along the bottom.
Once the kettle is boiling and the leaves are in the bottom of the bowl, I pour the boiling water into the bowl, and how high depends on the tea. The more delicate the tea is, (read the greener the tea), the less I fill the bowl with the near boiling water.
If its a highly delicate and very green tea, I aim to just cover the leaves with the very hot water, and then let it sit for quite a while, and start cooling the water I would add to top it off. I do this because for some reason the hotter the water the leaves sit in the more likely they are to settle, but the greener the tea the more easily it tends to settle. I am also establishing a root, but the low amount of water allows it to cool before overly cooking the leaves. Once the water to add is cool enough I top off the bowl, and start drinking. I drink down to 1/3 the level or so and then top off with warmer water.
If the tea is darker i.e Hong Cha or Yancha, I follow roughly the same steps as above, except upon first filling the bowl instead of just covering the leaves, I fill the bowl half way or slightly more. This is because for some reason the darker the leaves, and more so with Yancha the less likely they are to settle from just this step. The water constantly used to top off the bowl is also always near boiling, but I still only drink down to roughly a third of total volume before refilling.
It is a great way to slowly enjoy a large cup of tea, but I should caution while similar flavor waves come through brewing grandpa style vs brewing in a teapot or gaiwan, the flavor when brewed Grandpa style tends to go quicker, providing the first few "infusions" with strong robust brews compared to when brewed with a teapot.
A bit more history on the term Grandpa style, I believe the term was coined by MarsalN of A Tea Addicts Journal. I have also arrived at this method through experimenting, and talking with those more experienced such as MarshalN about how to best carry out this method.