If you are familiar with Photoshop and layer styles, the closest equivalent to that in Illustrator would be the Appearance Panel. I would suggest doing some searches for that specifically on Youtube, and get a better understanding of how that works. In some ways it's actually more powerful than Photoshop's layer styles, but it can't replicate some of the more raster style effects that Photoshop can, such as bevels. Once you understand that you can create complex effects with the Appearance Panel as opposed to making all the shapes separately, that will be a good head start.
Next I would suggest learning how to use the pen tool. There are a number of tutorials on this as well. Thirdly, I would seek out some videos on using the Path panel.