I spent my first night wandering around aimlessly, until a zombie ate my face. For my second night, I ran through the woods until I found a small island in the middle of a lake connected to the main land by a thin strip of land. I killed the two skeletons I found there with my bare hands, almost dying in the attempt. Then I spent the rest of the night on the island, watching the zombies and spiders spawning in the distance along the lake shore. The island seemed like a safe place so I decided to make it my home.
I still didn't know how to make torches, since I decided to play the game for a while before looking on-line for assistance, so my only source of light was the moon or sun and my crafting options were limited to the few things I figured out by trial and error. The next day, I built a small open-air fort out of stone I mined from the side of a mountain using shallow shafts ... again, I couldn't go too deep because I had no coal and didn't know how to make torches.
My island fort was surprisingly safe, considering the lack of lighting and my general lack of knowledge, since monsters will not spawn close to the player or on water. For the first week, I didn't even have doors, so if a mob made it to the island, I would fight and kill it in my fort with a pickaxe, one of the few tools I'd figured out how to make on my own.