Bloom the yeast: Heat your milk to about 110°F. Any hotter and you will kill your yeast; much cooler and your yeast will take a very long time to activate. It should be warm to the touch. Pour the warm milk into the bowl of a stand mixer and add your sugar and yeast. Use a handheld whisk to combine. I like to set the bowl on top of a preheating oven to bloom, but your counter is fine, too. This takes about 10 minutes.
Mix the dough: Once the yeast has bloomed, add the oil, eggs and salt. Using a stand mixed fitted with a paddle attachment for gluten-free flour, mix on low speed to break up the eggs and to combine all the ingredients. If you're using traditional flour, switch to the dough hook attachment. Add the flour and mix on low speed until all the ingredients are combined and the dough has come together into a cohesive ball, 1 to 2 minutes.
Gluten-free dough rises fairly quickly and is very tender, so you don't need to knead it or let it rise between mixing the dough and rolling our and shaping the final product. For traditional flour, you'll need to let the dough rise — there are many different approaches to this. I like to set the bowl of dough on top of a preheating oven. This works well and moves the process along pretty quickly. If you need to speed up the rise time, put a clean towel or some plastic wrap over the bowl to keep the dough warmer. You can also fill your sink with about 5 inches of warm water, cover the dough with a clean tea towel, and set the bowl in water. Your dough is ready to use when it looks as if it has doubled in size. When you press the dough a little, it should feel supple, soft, and have some more give. Yeast stays busy and dough rises when it is warm, so do your best to keep a warm environment for the dough as it rises.
At this point, you are ready to make buns of your choosing.