There are several ways to get around the world of Minecraft.
Horses are the best and fastest way to get around on land. With a donkey or a mule, you can carry your stuff around too!
Pigs can also be ridden, at a pinch! You'll need a saddle, which you can find in treasure chests in dungeons.
Place the saddle on a pig, climb on wiht a right click, and you can go anywhere the pig wants to take you.
Boats are the fastest way to travel the oceans. Build a boat, place it in the water and right-click to get in. You'll soon learn how to steer it. Bumping into land at high speed will often break the boat so be careful.
Build railways for travel and cargo.