Project management is not a new idea.  As long as things have needed to get done, people have needed to come up with a plan for how to do them.  There are few things worse than having something that needs to get done and not knowing who is supposed to be working on it or what the steps are in getting it done.  To get started with project management, you don't need any special skill sets or certain software (however there are many tools out there that can assist you), you just need to start with a few basic steps.

• What needs to be done - You probably have a long list of tasks that you know need to be completed.  The first thing is to organize these tasks by project in order to better keep track of them.  This can be done in a simple word processing document or a spreadsheet or even just with pen and paper. 
  
• Who needs to do it - Now that you have a better handle on what you need done, you need to make sure that you know who's going to do it.  By assigning people to tasks, you can accomplish two things:  You will know that someone is working on a task and that they are responsible for it, and you will be able to make sure that people are not getting overloaded by taking on too many tasks while others aren't working on as many things.  
• When it needs to be done - Arguable the most important of the steps is setting the timeline for when things need to be done.  Each task should be assigned the day that it is due and how much time is alotted to work on it.  By doing this, you can see what are the prioritized tasks as well as if you have many tasks that need to be completed at the same time so you don't get overwhelmed when a deadline approaches.  

As mentioned before, it is not required to use any special software to start with project management, but you may find that there are tools out there that are very useful to you.  Some of these software packages will better let you manage the people or resources that you have assigned to tasks, see a visual calendar of your timelines (one example is a gantt chart).  Tools have been designed as web-based and desktop-based; free, subscription based, or flat fee; for one person working on it or for sharing with multiple users - there is a great chance of finding a tool out there that works for you.  You can find a list of different project managment software at this site and also by searching for "project management software" in your favorite search engine.