Advice for a beginning/amateur photographer

Hi guys, I don't really know where to begin but here goes, I've recently taken up an interest in photography and although I usually don't have a lot of time on my hands I do like to take pictures every chance I get. I didn't really have much of an interest in photography in high school because money was tight and it seemed that an old small camera I had was inferior to the DSLRs that many of my classmates were using. That being said I don't have many pictures and want to start taking more photos because someday I'd like to be able to look back on pictures I took (sorta like the intro on HIMYM, lame but whatever). What sparked my interest in photography was a picture of tenor saxophonist Dexter Gordon taken by Herman Leonard at the Royal Roost in New York City whilst having a cigarette. It was not until I saw a documentary by Donald Weber about photographing the Fukushima Nuclear disaster that I decided to invest in a Canon SX160 (on sale during black friday). My current schedule prevents me from taking intro to photography classes but I still really want to explore this as a hobby. Any suggestions on what to do to improve my photography skills or where to go from here? Any advice for an amateur photographer is appreciated, thanks.