Combine water, yeast and sugar and let sit for 10 minutes. If your yeast mixture doesn't bubble up, your yeast is not active anymore. You will need to get new yeast.
In a large mixing bowl or a stand mixer add flour, sugar, salt to combine (dry ingredients)
In your dry ingredients mixture, add your yeast mixture, vegetable oil, and eggs
Using the dough attachment in your stand mixer, mixed until combine (about 6-10 minutes). Keep some extra flour handy. If your dough seems too wet, add a little bit of flour at a time until it comes together into a dough ball nicely without being too sticky.
Let the dough rise in an oiled bowl covered for about 1.5 hours
After 1.5 hours, take the dough out of the bowl and divide into 3 or 6 equal pieces and roll into long logs. (You can braid challah in many different ways. Try with 3 pieces and make a regular braid)
Put the 3 or 6 pieces of dough log parallel to each other on the baking sheet you are baking it on and pinch the top of the 3 or 6 pieces together
Braid the 3 pieces of dough like you would if you were braiding your hair
Once you are done braiding cover gently with a clean kitchen towel. Let rise for another hour.
Once the hour is up, preheat your oven to 350F (176C). Whisk your egg white you reserved with a spoonful of water and brush on top of the unbaked challah bread. Bake for about 30 minutes. Turning the pan 180 degrees at about the 15 minutes point (and brushing with more egg white solution when you turn the pan)
Remove the bread from the oven, let cool on a cooling rack. Slice and enjoy!