How do I start a PCB designing?

First, you need to find the right PCB design tool. Eagle CAD is good for beginners. Altium is used in the expert level. Refer to the Online tutorials for PCB design using Eagle CAD. Here are few resources that may help you out:
1. Tutorial Series for CadSoft Eagle
2. EAGLE
Once you get familiar with the Eagle software and if you have created your first .brd file, move the PCB fabrication process. There are several DIY methods available for the fabrication process out of which two method is simple, cheap and effective.
1. Toner transfer method in which the board file printed in a paper and transferred to the PCB using the iron box or laminator. This video might help you out in understanding the process: 

2. The second method is developed by Saipraveen Durairaman which is more reliable than the above method. This board file is printed in the form of vinly stickers and the stickers are pasted on the PCB. 

I would suggest you buy an epoxy PCB for all your fabrication is the process as it is more rugged and effective than the cheap one.

Happy PCB making!