I solved my first rubik's cube, but....?

With all the instructions surfing on youtube, I came upon a simple video that teaches exactly how to solve it.. It took me 15 hours to finally solve the puzzle, but I'm not satisfied.. Although, I can finally solve the cube, I have to write down the algorithms on a piece of paper because my memory is not that great. Question: How do people solve the puzzle in less than 30 seconds? To me, it's completely impossible.. A very scramble cube takes me 30 minutes tops to solve one... What am I doing wrong? Should I put the cube aside for the moment and come back to it later? I literally spent the whole day solving this piece, and my forearms starting to build some muscle. Instead of being excited solving this puzzle, I feel I didn't accomplish anything.