By making great phones. Lets not pretend here that Samsung copying the sunflower icon for the photo app and having a connector that looks like the apple one had a major impact on anyone's sales.
Edit: downvotes... you guys honestly think that the reason why Samsung has been successful is because of touchwiz? Most people don't even like Samsung's modifications to stock Android. It was stupid of them to make the changes they did, and they deserve a fine, but it certainly didn't help them much in terms of sales.
You are right though. Even though Touchwiz was an abomination compared to the smooth and slick iOS, Samsung's Galaxy S phone was a step ahead in every direction compared to the iPhone. At the time, it was the thinnest, lightest and the most powerful phone. Not the mention, the gorgeous display it had. Samsung innovated on every platform except the homescreen UI (sadly, many people don't see this).
But above all, their marketing and advertising strategy was unparalleled. I saw a Galaxy ad literally on every road, every TV show, every soccer match and what not! The success was not surprising given how much they effort they put.
Edit: downvotes... you guys honestly think that the reason why Samsung has been successful is because of touchwiz? Most people don't even like Samsung's modifications to stock Android. It was stupid of them to make the changes they did, and they deserve a fine, but it certainly didn't help them much in terms of sales.