Any Professional logo starts with a brainstorming or another creative method, continues with pen and paper, and finally, the computer.
But please, don't become a "i'll do your professional logo for 5$" guy, this is the kind of things who kills brands, enterprises, and our profession.
Now that is the way to do it!! Good to see somebody speak about pen and paper before even thinking to start on the computer!!
Learn Illustrator or Coreldraw, depends in what business you want to end up, web or print. Forget photoshop, waste of time for professional logo's!
First you have to brainstorm, have a face to face meeting with your client and
fully understand what he wants, what his business is about, what it reflects, who his competition is .... then most of the time you will have to try convince them that they ideas they have in their head not the way to do it. (for example: just because McDonalds has a red/yellow logo that doesn't mean that red/yellow is going to be good for his business!!) You are the professional, you will have to convince him what works and not!
You have to
fully understand what he wants before you start brainstorming, this will help you a lot in the process. Nothing worse then showing up to a client with a logo and see the look on his face that he didn't like it and that it's not what "he wanted".
Then you go to pen and paper, wright down all the keywords that reflext to the logo and try to come up with something creative and original. Don't be afraid to spend a few days on this process and try different ideas. What helps is to use google images or design books to see what logo's are allready out there. Please don't go for the obvious logo's: for example when you have to make a logo for a petshop don't include a picture of cat and a dog, BE ORIGINAL!
Why pen and paper? Because it's way easier and faster to brainstorm and try out some stuff. Once you have the idea you go to your computer and start transforming the logo you have on paper into vector. Make it clear for your client that you don't work for free, i give my clients 3 variations on a logo with 3 retoutches, if they want more retoutches after they will have to pay. Don't work FOR FREE!!! Make that completely clear from the beginning, your time costs money, don't fall for the design crodwsurfing shit like 99 designs who rape designers and give the business a bad name!!
Creating a professional logo takes time and you will have to study a lot!! Remember these 2 important things BE CREATIVE AND DON'T WORK FOR FREE!! Good luck!