You've probably suvived your first few nights, have at least iron tools, and have built up a base you are proud of. But you want more. The best way to do that is to explore. Before you go off, it would be smart to make a map with 9 paper. You should also make a tall pillar so you know when you reach home, sweet home. My last bit of advice is to leave a trail of blocks that can't naturally generate so you have a path home. Once you do that, you can explore as much as you want! Watch out for creepers!
Villagers may sell you maps to exotic locations, such as this woodland mansion.