Like learning an instrument, it's not just a short course to learn the software, and like music some people have an ear for it and others don't.
You can find tutorials all over the web, the most recommended would be Lynda.com - and it's a paid subscription.
Software is Adobe -
Software and services for creative professionals | Adobe Creative Cloud which you subscribe to monthly.
3 pieces of software required
Illustrator - for vector logos and images
Photoshop - for manipulating photographs
InDesign - for page layout and creating print ready artwork
What you see on screen isn't what necessarily prints, what looks good on the monitor may not print right.
Printing companies charge a premium for fixing artwork that is not print ready.
There's more to design than learning programs, and there's more to the programs than meet the eye.
If you're willing to invest a year and a a few hundred quid in software and training then that's up to you.
But you really should find a better way to articulate your ideas to your designer(s) or find another designer.
There are no shortcuts in this industry - not everyone that buys a mixing deck ends up being a top dj - and not everyone that picks up a guitar sells out arenas.
Your time and money would be better spent by
Articulating what you want the way you'd describe it to a 4 year old
Researching images of similar style to what you want to emulate
Creating a colour mood board to send on to your designer
Searching through some fonts that you like (but not necessarily will use)
Selecting logos or other icons that you find interesting (but won't use but just like)