If you die without a bedroll...or bed, whatever you want to call it, you will spawn randomly in the world. This is something you want to take care of quickly as it can make for really tough gameplay without a good spawn point.
You will need to craft a bed using cotton plants. Once you have accumulated enough cotton, craft it into cloth, cloth in turn can craft a sleeping bag. HOLY CRAP! You just made a bed! You're not done yet though, don't get too excited you little noob. You need to place this down by placing the sleeping bag in your tool belt. You know...that thing at the bottom of the screen. Once in your hand, look at the ground and left click to throw that S.o.B down.
A good idea is to get to a safe place immediately and place this down there so when you die you'll respawn there. Keep in mind, you won't always be at a safe place quickly so a word of advice is to keep this on your tool belt for an emergency. If you are about to die, place it down so that you do not spawn far away from where you were.