There are entire professions devoted to recording and mixing (I'm in one of them). I don't think a couple of paragraphs are going to do it in order to get you where you need to be. I'd recommend taking the time to learn some theory and practical knowledge. The most important part is experience... and you only get that from trying and making mistakes. I made several with EQ and compression when I first tried home recording back in 1991.
My first recommendation would be to buy a decent audio interface. I'd shoot for something in the $300 range for a beginner. This will dramatically improve your results once you've mastered gain-staging. I would also invest in a DAW. Reaper is surprisingly affordable at around $50US for non-professional use. The great thing about a DAW is that you can EQ, compress, etc. inside of the DAW... save all your settings... and then revise your mix later on. You'll also find it valuable for learning and practicing.
A quality pair of headphones and if you can afford them a quality pair of monitors will help. Bear in mind that when using speakers, the room that the speakers are in will ultimately impact what you're hearing with your ears.