Dedicated Server costs vary greatly. Anywhere from ~$50/mo to ~$1,500/mo with the average being around $150-$200/mo.
It all depends on what resources you need, and how reliable you want it to be.
The first thing you need to consider is how much CPU, RAM, Drive space, Bandwidth you need and if you need an unmanaged or managed server. This will let you know what to look for and you can start shopping around.
The next thing you need to consider is how reliable you need it to be. There are several places where you can find servers for cheap. However, there are downfalls to this as well. Remember the old saying "You get what you pay for"! Many of the budget server providers provide services for cheap because they cut corners on their network and/or support.