There's more to designing a logo than one may think. A logo should represent it's owner's company and brand identities.
Photoshop , Illustrator and/or other vector applications are the tools needed but you have to be knowledgeable of their use.
In terms of tutorials, it would be difficult to outline a specific one for you as it would be dependent on the design you have in mind. But here's a few to give you inspiration for logo ideas and start you on your way.
Here is the main reason why you should not be using Photoshop for creating logos.
Photoshop can not create true vector images. Photoshop does have so called vector tools and can save some vector content in some formats, however, Photoshop will never create a true vector file. Regardless of how you create a file and save it, Photoshop always saves both vector and raster information. You can't create vector files with Photoshop. What Photoshop creates are vector containers with raster content. This is much different than a vector container with a vector content. If a square has a gradient fill. That gradient fill is raster based and it will suffer when scaling.
A vector based program like Illustrator, will create a vector shape with a vector gradient within that shape. That means when the shape is resized upon output, the gradient is recalculated to match the new boundaries. What Photoshop does is, upon output, it recalculates the vector container but only scales the raster contents in the container. This can result in "broken pixels" for the interior appearance.
I agree with the suggestions above. Adobe Illustrator is a great place to start. I do occassionally have to us a combination of Photoshop and Illustrator but your main program is going to be Illustrator unless you want to use Corel draw. I don't know much about Corel Draw. I create logos with my graphic design business and I would suggest this tutorial http://www.creativebloq.com/digital-art/illustrator-tutorials-1232697 It covers basic tools in Illustrator all the way to logo design. If you are new to Illustrator I liked using Adobe Illustrator Classroom in a book and The Adobe Illustrator WOW book are both great resources. They both come with a cd and are very comprehensive in teaching the program. Make sure you find one that matches the version of Illustrator you are using.