For the yeast to be vegan, make sure it does not contain E491 (Sorbitan monostearate) which may or may not be from animal source. Or check with the manufacturer to be safe.
Preheat your oven to 170-200C (340-390F).
Add flour, salt, and yeast and mix well. Then add the water and the oil. Start mixing everything together. I suggest using a spoon in the beginning as it is usually very hard to mix. After a while you should be able to use your hands.
Make sure everything is kneaded well and you should have a nice and flexible dough. Add teaspoons of flour at a time if it is too sticky.
Put it in a bowl with a kitchen towel covering it. Let it rest in a warm place for half an hour. It should double in size.
You can try substituting parts of the all-purpose flour with whole-grain flour. 1/3 or 2/3 work fine, but it gets harder and less fluffy.
Prepare the sauce by adding some water to the tomato paste. Just enough so it is liquid again but not to watery and you can easily spread it later. Add lots of herbs, pepper and some salt.
Line a backing tray with non-stick cooking paper.
After the half hour is up, spread the dough with your hands.
Put the sauce on top with a spoon and make sure to get it to edges of the dough (they will turn hard otherwise).
Add whatever vegan cheese and toppings (in that order) you like.
Bake for about 20 minutes around 170-200C (340-390F) with lower and upper heat + ventilator going. The length and temperature differs from oven to oven. Just watch it carefully every couple of minutes so it doesn't burn.

For the dough:
300g (or 2/3 pound) all-purpose flour
1 teaspoon salt
1 pack dry instant yeast (around 7g or 2 teaspoon)
2 tablespoon olive oil (any other should work as well)
170ml (or 3/4 cup) warm water

For a standard sauce:
130g (4.5oz) concentrated tomato paste
Italian herb (at least thyme and oregano)
salt & pepper