Minecraft wiki entry for Survival_in_an_infinite_desert, associated text: Find dirt or craft sandstone or find a small cave for shelter on your first day, otherwise you can die on your first night because you can't make a roof.
Don't fight anything, if you can help it. You're too weak. Use defensive structures and only ever fight with a strong defensive advantage.
If structures are allowed, find a village as soon as possible and use/steal the crafting table and furnace. Requisition some of the torches. Loot the chests. Ingots or diamonds for making tools are a top priority. Loot the crops too, but always replant what you take.
Get out of villages - especially large villages - before dusk so you don't trigger mob attacks on them. Guard the villagers carefully so you can trade with them. Stay out of the village at night until you have made the villagers totally safe.
The most likely way to "Advance to the Stone Age" is either to find an iron pickaxe in a smith's chest; or to get a village crafting table, and then craft one from ingots from village chests or dropped by mobs; or trick a creeper into "mining" some cobblestone for you and craft a stone pickaxe.
However you get one, getting a pickaxe is a critical breakthrough. Make a pickaxe out of diamond or gold if necessary, to collect your first cobblestone and enter the Stone Age.
Save your sticks (from dead bushes) for making tools and weapons. They're too rare and valuable to use as fuel unless there are no villages to provide furniture to burn.
Save your furnace fuel for smelting ore, not cooking food. Eat raw food. It's, er, good for you.
Save your first iron for making a bucket - use stone tools, not iron tools, because stone doesn't use fuel, and you are incredibly short of fuel.
Once you have a bucket, use lava for fuel and go crazy with the furnace. Smelting! Cooked food! Yes, the Bucket Age is the high-point of Desert Biome civilization.